RD SHARMA Solutions for Class 10 Maths Chapter 6 - Co-ordinate Geometry

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Chapter 6 - Co-ordinate Geometry Exercise 6.63

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 6

A line Segement is of length 10 units. If the coordinates of its one end are (2,3) and the abscissa of the other end is 10, then its ordinate is

(a) 9,6

(b) 3,-9

(c) -3,9

(d) 9,-6

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

So, the correct option is (d).

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 9

 Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Chapter 6 - Co-ordinate Geometry Exercise 6.64

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 2

If (-1,2),(2,-1) and (3,1) are any three vertices of a parallelogram, then

(a) a = 2, b = 0

(b) a = -2, b = 0

(c) a = -2, b = 6

(d) a = 6, b = 2

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

 

Note: The answer does not match the options.

Question 3

If A (5,3), B(11,-5) and P(12,y) are the vertices of a right triangle right angled at P, then y = 

(a) - 2,4

(b) -2 ,4

(c) 2, -4

(d) 2,4

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 4

The area of the triangle formed by (a,b+c), (b,c+a) and (c,a+b) is 

(a)  a+b+c

(b) abc

(c) (a+b+c)2

(d) 0

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 5

If (x,2),(-3,-4) and (7,-5) are collinear, then x = 

(a) 60

(b) 63

(c) -63

(d) -60

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 10

The line segment joining points (-3,4), and (1,-2) is divided by y - axis in the ratio

(a) 1 : 3

(b) 2 : 3

(c) 3 : 1

(d) 2: 3

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 11

The ratio in which (4,5) divides the join of (2,3) and (7,8) is 

(a) -2 : 3

(b) -3 : 2 

(c) 3 : 2

(d) 2 : 3

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 12

The ratio in which the x-axis divides the segment joining (3,6) and (12,-3) is

(a) 2:1

(b) 1 :2

(c) -2 : 1

(d) 1 : -2 

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 13

If the centrroid  of the triangle formed by the points (a,b),(b,c) and (c,a) is at the origin, then a3 + b3 + c3

(a) abc

(b) 0

(c) a+b+c

(d) 3abc

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 14

If points (1, 2), (-5, 6) and (a, -2) are collinear, then a =

(a) -3

(b) 7

(c) 2

(d) -2

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 15

If the centroid of the triangle formed by (7, x), (y, -6) and (9, 10) is at (6, 3), then (x, y) =

(a) (4, 5)

(b) (5, 4)

(c) (-5, -2)

(d) (5, 2)

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Chapter 6 - Co-ordinate Geometry Exercise 6.65

Question 1

The distance of the point (4, 7) from the x-axis is

(a) 4

(b) 7

(c) 11

(d) Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 1

We know, distance of point (x, y) from x-axis is y.

Hence, distance of point (4, 7) from x-axis is 7.

Hence, correct option is (b).

Question 2

The distance of the point (4, 7) from the y-axis is

(a) 4

(b) 7

(c) 11

(d) Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 2

We know distance of point (x, y) from y-axis is x.

Hence distance of point (4, 7) from y-axis is 4.

Hence, correct option is (a).

Question 3

If P is a point on x-axis such that its distance from the origin is 3 units, then the coordinates of a point Q on OY such that OP = OQ, are

(a) (0, 3)

(b) (3, 0)

(c) (0, 0)

(d) (0, -3)

Solution 3

Given P is a point on x-axis

Hence P = (x, 0)

Distance from the origin is 3

Hence P = (3, 0)

Given Q is a point on y-axis

So Q is (0, y)

Given that OP = OQ

implies OQ = 3

Distance of Q from the origin is 3

Hence y = 3

implies Q = (0, 3)

Hence, correct option is (a).

Question 4

If the point (x, 4) lies on a circle whose centre is at the origin and radius is 5, then x =

(a) ±5

(b) ±3

(c) 0

(d) ±4

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 5

If the point P (x, y) is equidistant from A(5, 1) and B (-1, 5), then

(a) 5x = y

(b) x = 5y

(c) 3x = 2y

(d) 2x = 3y

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 6

If points A (5, p), B (1, 5), C (2, 1) and D (6, 2) form a square ABCD, then p =

(a) 7

(b) 3

(c) 6

(d) 8

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 8

The coordinates of a point on x-axis which lies on the perpendicular bisector of the line segment joining the points (7, 6) and (-3, 4) are

(a) (0, 2)

(b) (3, 0)

(c) (0, 3)

(d) (2, 0)

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 9

If the centroid of the triangle formed by the points (3, -5), (-7, 4), (10, -k) is at the point (k, - 1), then k =

(a) 3

(b) 1

(c) 2

(d) 4

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 10

If (-2, 1) is the Centroid of the triangle having its vertices at (x, 2), (10, -2), (-8, y), then x, y satisfy the relation

a. 3x + 8y = 0

b. 3x - 8y = 0

c. 8x + 3y = 0

d. 8x = 3y

Solution 10

The Centroid of the triangle is given by

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

x=-8 and y=3 satisfy(a) 3x + 8y = 0.

Question 11

The coordinates of the fourth vertex of the rectangle formed by the points (0, 0), (2, 0), (0, 3) are

(a) (3, 0)

(b) (0, 2)

(c) (2, 3)

(d) (3, 2)

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 12

The length of a line segment joining A(2, -3) and B is 10 units. If the abscissa of B is 10 units, then its ordinates can be

(a) 3 or -9

(b) -3 or 9

(c) 6 or 27

(d) -6 or -27

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 13

The ratio in which the line segment joining P(x1, y1) and Q(x2, y2) is divided by x-axis is

(a) y1 : y2

(b) -y1 : y2

(c) x1 : x2

(d) -x1 : x2

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 14

The ratio in which the line segment joining points A(a1, b1) and B(a2, b2) is divided by y-axis is

(a) -a1 : a2

(b) a1 : a2

(c) b1 : b2

(d) -b1 : b2

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Chapter 6 - Co-ordinate Geometry Exercise 6.66

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

 

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 2

If the coordinates of one end of a diameter of a circle are (2, 3) and the coordinates of its centre are (-2, 5), then the coordinates of the other end of the diameter are

(a) (-6, 7)

(b) (6, -7)

(c) (6, 7)

(d) -6, -7)

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 3

The coordinates of the point P dividing the line segment joining the points A (1, 3) and B (4, 6) in the ratio 2 : 1 are

(a) (2, 4)

(b) (3, 5)

(c) (4, 2)

(d) (5, 3)

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

In the figure, the area of ΔABC (in square units) is

(a) 15

(b) 10

(c) 7.5

(d) 2.5

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 5

The point on the x-axis which is equidistant from points (-1, 0) and (5, 0) is

(a) (0, 2)

(b) (2, 0)

(c) (3, 0)

(d) (0, 3)

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 7

If P(2, 4), Q(0,3), R (3, 6) and S (5, y) are the vertices of a parallelogram PQRS, then the value of y is

(a) 7

(b) 5

(c) -7

(d) -8

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 8

If A(x, 2), B (-3, -4) and C (7, -5) are collinear, then the value of x is

(a) -63

(b) 63

(c) 60

(d) -60

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Chapter 6 - Co-ordinate Geometry Exercise 6.67

Question 1

If the point P(2, 1) lies on the line segment joining points A (4, 2) and B (8, 4), then

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 2

A line intersects the y-axis and x-axis at P and Q, respectively, If (2, -5) is the mid-point of PQ, then the coordinates of P and Q are respectively

a. (0, -5) and (2, 0)

b. (0, 10) and (-4, 0)

c. (0, 4) and (-10, 0)

d. (0, -10) and (4, 0)

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Chapter 6 - Co-ordinate Geometry Exercise Ex. 6.1

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry  Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Chapter 6 - Co-ordinate Geometry Exercise Ex. 6.2

Question 1

Show that ∆ABC, where A (-2, 0), B (2, 0) C (0, 2) and ∆PQR, where P (-4, 0), Q (4, 0), R (0, 4) are similar.

Solution 1

Using the distance formula,

AB=Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

AC=Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

BC=Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

PQ=Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

PR=Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

QR=Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Now,

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

ΔABC ~ ΔPQR

by the SSS test.

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 10


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 11

Show that the points A(1,-2), B(3,6), C(5,10) and D(3,2) are the vertices of a parallelogram.

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
Question 12

Prove that the points (1, 7), (4, 2), (-1, -1) and (-4, 4) are the vertices of a square.

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
Question 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 17

The points A(2, 9), B(a, 5) and C(5, 5) are the vertices of triangle ABC right angled at B. Find the values of a and hence the area of ABC.

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 25

Find a point which is equidistant from the points

A (-5, 4) and B (-1, 6). How many such points are there?

Solution 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 26

The centre of a circle is (2a, a - 7). Find the values of a if the circle passes through the point (11, -9) and has diameter Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometryunits.

Solution 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 27

Ayush starts walking from his house to office, Instead of going to the office directly, he goes to bank first, from there to his daughter's school and then reaches the office. What is the extra distance travelled by Ayush in reaching the office? (Assume that all distance covered are in straight lines). If the house is situated at (2, 4), bank at (5, 8) school at (13, 14) and office at (13, 26) and coordinates are in kilometer.

Solution 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 29

If (-4, 3) and (4, 3) are two vertices of an equilateral triangle, find the coordinates of the third vertex, given that the origin lies in the (i) interior (ii) exterior of the triangle.

Solution 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

 

Question 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
Question 31

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 31

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 32

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 32

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 33

Show that the points A(5,6), B(1,5), C(2,1) and D(6,2) are the vertices of a square.

Solution 33

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 34

Prove that the points A(2, 3), B(-2, 2), C(-1, -2), and D (3, -1) are the vertices of a square ABCD.

Solution 34



Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 35

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 35

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 36

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 36

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 37

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 37

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 38

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 38

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 39

If the point P(x,y) is equidistant from the points A(5,1) and B(1,5), prove that x = y.

Solution 39

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 40

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 40

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 41

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 41

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 42

If the point P(k-1, 2) is equidistant from the points A(3, k) and B(k, 5), find the values of k.

Solution 42

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 43

If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p. Also, find the length of AB.

Solution 43

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 44

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 44

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 45

Find the equation of the perpendicular bisector of the line segment joining points (7,1) and (3,5).

Solution 45

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 46

Prove that the points (3,0), (4,5), (-1,4) and (-2,-1), taken in order, form a rhombus. Also, find its area.

Solution 46

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 47

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 47

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 48

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 48

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 49

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 49

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 50

If a point A(0,2) is equidistant from the points B(3,p) and C(p,5), then find the value of p.

Solution 50

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 51

Prove that the points (7, 10), (-2, 5) and (3, -4) are the vertices of an isosceles right triangle.

Solution 51

 


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry



Question 52

If the point P(x, 3) is equidistant from the points A(7, -1) and B(6, 8), find the value of x and the find the distance AP.

Solution 52



Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 53

If A(3, y) is equidistant from the points P(8, - 3) and Q(7, 6), find the value of y and find the distance AQ.

Solution 53



Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 54

If (0, -3) and (0, 3) are the two vertices of an equilateral triangle, find the coordinates of its third vertex.

Solution 54

For an equilateral triangle, the perpendicular bisector of any side passes through the opposite vertex.

Both the points, (0, -3) and (0, 3), lie on the y-axis equidistant from the origin. Hence, the perpendicular bisector joining these two points is the x-axis.

Any point on the x-axis has the coordinates (a, 0).

The distance between (0, -3) and (0, 3) is 6.

Hence, the distance between (a, 0) and (0, 3) should also be 6.

62 = (a - 0)2 + (0 - 3)2

36 = a2 + 9

a2 = 27


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry


Question 55

If the point P(2, 2) is equidistant from the points A(-2, k) and B(-2k, -3), find k. Also, find the length of AP.

Solution 55

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 56

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 56

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 57

Find the circumcentre of the triangle whose vertices are (-2,-3), (-1,0), (7,-6).

Solution 57

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 58

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 58

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
Question 59

Find the centre of the circle passing through (5, -8), (2, -9) and (2, 1).

Solution 59

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 60

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 60

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 61

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 61

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 62

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 62

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Chapter 6 - Co-ordinate Geometry Exercise Ex. 6.3

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 2

Find the points of trisection of the line segment joining the points:

(i) (5, -6) and (-7, 5), (ii) (3, -2) and (-3,-4), (iii) (2,-2) and (-7,4).

Solution 2

(i)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

(ii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

(iii)

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 5

If P(9a - 2, -b) divides the line segment joining A(3a + 1, -3) and B(8a, 5) in the ratio 3 : 1, find the values of a and b.

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 6

If (a, b) is the mid-point of the line segment joining the points A (10, -6), B(k, 4) and a - 2b = 18, find the value of k and the distance AB.

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 9

If the points P,Q(x, 7), R, S(6, y) in this order divide the line segment joining A(2, p) and B (7, 10) in 5 equal parts, find x, y and p.

Solution 9

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry 

 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry 

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry 

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry 

Question 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
 
 
*Note: (i) Answer given in the book is incorrect.
Question 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 17

Prove that (4,3), (6,4), (5,6) and (3,5) are the angular points of a square.

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 20

Find the ratio in which the line segment joining the points A (3, -3) and B (-2, 7) is divided by x- axis. Also, find the coordinates of the point of division.

Solution 20

Let the point on the x-axis be (a, 0).

Let this point divide the line segment AB in the ratio of r : 1.

Using the section formula for the y-coordinate, we get

 



Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 21

Find the ratio in which the point P(x, 2) divides the line segment joining the points A (12, 5) and B (4, -3). Also, find the value of x.

Solution 21

 



Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 22

Find the ratio in which the point P(-1, y) lying on the line segment joining A(-3, 10) and B(6, -8) divides it. Also find the value of y.

Solution 22




Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 26

In what ratio does the point (-4,6) divide the line segment joining the points A(-6,10) and B(3,-8)?

Solution 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 31

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 31

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 32

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 32

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 33

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 33

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 34

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 34

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 35

Show that the points A(1,0) B(5,3), C(2,7) and D(-2,4) are the vertices of a parallelogram.

Solution 35

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 36

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 36

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 37

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 37

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 38

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 38

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 39

Points P, Q, R and S divide the line segment joining the points A(1, 2) and B(6, 7) in 5 equal parts. Find the coordinates of the points P, Q, and R.

Solution 39

The difference between the x-coordinates of A and B is 6 - 1 = 5

Similarly, the difference between the y-coordinates of A and B is 7 - 2 = 5

Hence, if the line segment joining A(1, 2) and B(6, 7) is divided into 5 equal parts by the points P, Q, R and S, then the coordinates of P, Q, R and S can be found out by increasing the x and the y coordinates of A by 1 successively.

Hence, the coordinates of P are (1 + 1, 2 + 1) = (2, 3)

The coordinates of Q are (2 + 1, 3 + 1) = (3, 4)

The coordinates of R are (3 + 1, 4 + 1) = (4, 5)

 

Question 40

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 40

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 41

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 41

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 42

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 42

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 43

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 43

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 44

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 44

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
Question 45

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 45

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 46

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 46

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 47

If two vertices of a parallelogram are (3,2), (-1,0) and the diagonals cut at (2,-5), find the other vertices of the parallelogram.

Solution 47

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 48

If the coordinates of the mid-points of the sides of a triangle are (3,4), (4,6), and (5,7), find its vertices.

Solution 48

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 49

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 49

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 50

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 50

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
Question 51

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 51

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 52

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 52

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 53

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 53

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 54

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 54

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 55

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 55

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry


Question 56

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 56

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 57

A point P divides the line segment joining the points A(3,-5) and B(-4,8), such that Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry . If P lies on the line x + y = 0, then find the value of k.

Solution 57

Given points are A(3,-5) and B(-4,8).

P divides AB in the ratio k : 1.


Using the section formula, we have:

Coordinate of point P are {(-4k+3/k+1)(8k-5/k+1)}

Now it is given, that P lies on the line x+y = 0

Therefore,

-4k+3/k+1 + 8k-5/k+1 =0

=> -4k+3+8k-5 =0

=> 4k -2 =0

=> k=2/4

=> k=1/2

Thus, the value of k is 1/2.

Question 58

The mid - point P of the line segment joining the points A (-10, 4) and B (-2, 0) lies on the line segment joining the points C (-9, -4) and D (-4, y). Find the ratio in which P divides CD. Also, find the value of y.

Solution 58




Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 59

If the point C(-1, 2) divides internally the line segment joining the points A(2, 5) and B(x, y) in the ratio 3 : 4, find the value of x2 + y2.

Solution 59

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 60

ABCD is a parallelogram with vertices A(x1, y1), B(x2, y2) and C (x3, y3). Find the coordinates of the fourth vertex D in terms of x1, x2, x3, y1, y2 and y3.

Solution 60

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 61

The points A (x1, y1), B(x2, y2) and C (x3, y3) are the vertices of ABC.

 i. The median from A meets BC at D. Find the coordinates of the point D.

 ii. Find the coordinates of the point P on AD such that AP : PD = 2 : 1.

 iii. Find the points of coordinates Q and R on medians BE and CF respectively such that BQ : QE = 2 : 1 and CR : RF = 2 : 1.

 iv. What are the coordinates of the centroid of the triangle ABC

Solution 61

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Chapter 6 - Co-ordinate Geometry Exercise Ex. 6.4

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
Question 7

Prove analytically that the line segment joining the middle points of two sides of a triangle is equal to half of the third side.

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Chapter 6 - Co-ordinate Geometry Exercise Ex. 6.5

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 4

Find the area of the quadrilaterals, the coordinates of whose vertices are

(-4,-2), (-3,-5), (3,-2), (2,3)

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry
Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 8

Find the area of a quadrilateral ABCD, the coordinates of whose vertices are A(-3, 2), B(5, 4), C(7, -6) and D(-5, -4).

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 9

In ABC, the coordinates of vertex A are (0, -1) and D(1, 0) and E(0, 1) respectively the mid-points of the sides AB and AC. If F is the mid-point of side BC, find the area of DEF.

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry 

Question 10

Find the area of the triangle PQR with Q (3, 2) and the mid-points of the sides through Q being (2, -1) and (1, 2).

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry 

 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 11

If P(-5, -3), Q(-4, -6), R(2, -3) and S(1, 2) are the vertices of a quadrilateral PQRS, find its area.

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 12

If A (-3, 5), B(-2, -7), C(1, -8) and D(6, 3) are the vertices of a quadrilateral ABCD, find its area.

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry


Question 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 15

If the vertices of a triangle are (1,-3), (4,p) and (-9, 7) and its area is 15 sq. units, find the value (s) of p.

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 22

Find the value of a for which the area of the triangle formed by the points A(a, 2a), B(-2, 6) and C (3, 1) is 10 sequare units.

Solution 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 23

If a ≠ b ≠ 0, prove that the points (a, a2), (b, b2), (0, 0) are never collinear.

Solution 23

Let the points (a, a2), (b, b2), (0, 0) represent a triangle. If we can prove that the area of the triangle so formed is not equal to zero, then we can prove that the points (a, a2), (b, b2), (0, 0) are never collinear.

Area of a triangle is given by

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Now b≠a≠0.

So,

b - a≠0,

Δ≠0

Thus, points (a, a2), (b, b2), (0, 0) are never collinear.

Question 24

The area of a triangle is 5 sq. units. Two of its vertices are at (2, 1) and (3, -2). If the third vertex is (7/2, y), find y.

Solution 24

Area of a triangle is given byRd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry 

Question 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 31


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Solution 31


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 32

Find the value (s) of k for which the points (3k - 1, k - 2), (k, k - 7) and (k - 1, -k - 2) are collinear.

Solution 32


Let the points be A, B and C respectively.

If A, B and C are collinear, then the area of ∆ABC is zero.



Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry




Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 33

If the points A(-1, -4), B(b, c) and C(5, -1) are collinear and 2b + c = 4, find the values of b and c.

Solution 33



Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 34

If the points A(-2, 1), B(a, b) and C(4, -1) are collinear and a - b = 1, find the values of a and b.

Solution 34


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 35

If the points A(1, -2), B(2, 3), C(a, 2) and D(-4, -3) form a parallelogram, find the value of a and height of the parallelogram taking AB as base.

Solution 35

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 36

A(6, 1), B(8, 2) and C(9, 4) are three vertices of a parallelogram ABCD. If E is the mid-point of DC, find the area of ADE.

Solution 36

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Question 37

If D(-1/5, 5/2), E(7, 3) and F(7/2, 7/2) are the mid-points of sides of ABC, find the area of ABC

Solution 37

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry 

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Co Ordinate Geometry

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