Chapter 8 : Co-ordinate Geometry - Rd Sharma Solutions for Class 9 Maths CBSE

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Chapter 8 - Co-ordinate Geometry Excercise Ex. 8.1

Question 1

Plot the following points on the graph paper:

(i) (2,5)

(ii) (4,-3)

(iii) (-5,-7)

(iv) (7,-4)

(v) (-3,2)

(vi) (7,0)

(vii) (-4,0)

(viii) (0,7)

(ix) (0,-4)

(x) (0,0)

Solution 1

The graph of the given points are:

Question 2

Write the coordinates of each of the following points marked in the graph paper:

Solution 2

The coordinates of the given points are A(3,1), B(6,0), C(0,6), D(-3,0), E(-4,3), F(-2,-4), G(0,-5), H(3,-6), P(7,-3) and Q(7,6)

Chapter 8 - Co-ordinate Geometry Excercise 8.7

Question 1

The Point of intersection of co-ordinate axes is

(a) ordinate (b) abscissa   (c) quadrant  (d) origin

Solution 1

The point of intersection of co-ordinate axes i.e. X-axis and Y-axis is (0, 0), which is called origin.

Hence, correct option is (d).

Question 2

The abscissa and ordinate of the origin are

(a) (0, 0)  

(b) (1, 0)

(c) (0, 1)  

(d) (1, 1)

Solution 2

begin mathsize 12px style Origin space equals open parentheses 0 comma 0 close parentheses
abscissa space equals space intercept space on space straight X minus axis space equals space 0
ordinate space equals space intercept space on space straight Y minus axis space equals space 0
rightwards double arrow open parentheses 0 comma space 0 close parentheses space is space the space answer.
Hence comma space correct space option space is space left parenthesis straight a right parenthesis. end stylebegin mathsize 12px style blank end stylebegin mathsize 12px style blank end style

Question 3

The measure of the angle between the coordinate axes is

(a) 0o    (b) 900   (c)1800      (d)3600
Solution 3

The space angle space between space the space co minus ordinate space axes space is space 90 degree space because space straight X minus axis space perpendicular space straight Y minus axis.
Hence comma space correct space option space is space left parenthesis straight b right parenthesis.

Question 4

A point whose abscissa and ordinate are 2 and -5 respectively, lies in 

(a) First quadrant

(b) Second quadrant

(c) Third quadrant

(d) Fourth quadrant

Solution 4

Abscissa is = 2 (positive intercept on X-axis)

and ordinate = -5 (negative intercept on Y-axis)

so X-value is positive and Y-value is negative, i.e. Fourth Quadrant.

Hence, correct option is (d).

Question 5

Point (-4, 0) and (7, 0) lie

(a) on X- axis

(b) on Y- axis

(c) in first quadrant 

(d) in second quadrant


Solution 5

In (-4, 0) and (7, 0 ),

measure of ordinate = 0

That means, intercept on Y-axis = 0

So, points lies on X-axis.

Hence, correct option is (a).

Question 6

The ordinate of any point on X-axis is

(a) 0

(b) 1

(c) -1

(d) any number

Solution 6

On X- axis, all points have their  Y- intercept = 0

So their ordinate = 0

Hence, correct option is (a).

Question 7

The abscissa of any point on Y-axis is

(a) 0

(b) 1

(c) -1

(d) any number

Solution 7

Every point on Y-axis have X-intercept = 0

Thus, their abscissa = 0

Hence, correct option is (a).

Question 8

The abscissa of a point is positive in the

(a) First and Second quadrant

(b) Secod and Third quadrant

(c) Third and Fourth quadrant

(d) Fourth and First quadrant

Solution 8

Abscissa = Intercept on X-axis

If intercept on X-axis is positive, means First and Fourth quadrant.

Hence, correct option is (d).

Question 9

A point whose abscissa is -3 and ordinate 2 lies in

(a) First Quadrant

(b) Second Quadrant

(c) Third Quadrant

(d) Fourth Quadrant

 

Solution 9

begin mathsize 12px style If space abscissa space equals space minus 3
Intercept space on space straight X minus axis space equals space minus 3
straight X space less than 0
and space Ordinate space equals space 2
Intercept space on space straight Y space axis space is space equals space 2
straight Y space greater than 0
So comma space Point space is space in space Second space Quadrant.
Hence comma space correct space option space is space open parentheses straight b close parentheses. end style

Question 10

Two points having same abscissae but different ordinates lie on

(a) X-axis

(b) Y-axis

(c) a line parallel of Y-axis

(d) a line parallel to X-axis

Solution 10

Let two points be (a, b) and (a, c).

If abscissa is same = a

and ordinate is different then all such points will lie on a line parallel to Y- axis because value of X-intercept  

i.e. abscissa is fixed.

Hence, correct option is (c).

Question 11

The perpendicular distance of the point P (4, 3) form x-axis is

(a) 4

(b) 3

(c) 5

(d) None of these

Solution 11

begin mathsize 12px style If space perpendicular space drawn space from space straight P space to space straight X minus axis comma space then space the space perpendicular space is space equal space to space
measure space of space ordinate space of space point space straight P.
So comma space perpendicular space distance space of space point space straight P space form space straight X minus axis space equals 3
Hence comma space correct space option space is space open parentheses straight b close parentheses. end style

Question 12

The perpendicular distance of the point P(4, 3) from y-axis is

(a) 4

(b) 3

(c) 5

(d) none of these

Solution 12

begin mathsize 12px style If space we space draw space straight a space perpendicular space from space point space straight P open parentheses 4 comma space 3 close parentheses space to space straight Y minus axis comma
the space measure space of space perpendicular space is space equal space to space abscissa space of space point space straight P.
So space perpendicular space distabce space form space straight Y minus axis space equals space abscissa space equals space 4
Hence comma space correct space option space is space open parentheses straight a close parentheses. end style

Question 13

The distance of the point P(4, 3) from the origin is

(a) 4

(b) 3

(c) 5

(d) 7

Solution 13

Error converting from MathML to accessible text.

Question 14

The area of the triangle formed by the points A(2, 0), B(6, 0) and C(4, 6) is

(a) 24 sq. units

(b) 12 sq. units

(c) 10 sq. units

(d) none of these

Solution 14

Error converting from MathML to accessible text.

Question 15

begin mathsize 12px style The space area space of space the space triangle space formed space by space the space points space straight P open parentheses 0 comma space 1 close parentheses comma space straight Q open parentheses 0 comma space 5 close parentheses space and space straight R open parentheses 3 comma space 4 close parentheses space is
open parentheses straight a close parentheses space 16 space sq. space units
open parentheses straight b close parentheses space 8 space sq. space units
open parentheses straight c close parentheses space 4 space sq. space units
left parenthesis straight d right parenthesis space 6 space sq. space units end style

Solution 15

begin mathsize 12px style PQ space equals space 4 space units
Let space RS thin space be space perpendicular space drawn space from space straight R space to space PQ.
Length space of space RS space equals space abscissa space of space straight R open parentheses 3 comma space 4 close parentheses
rightwards double arrow RS space equals space 3 space units
Area space of space triangle RQP space equals 1 half cross times PQ space cross times RS space equals 1 half cross times 4 space cross times 3 space equals space 6 space sq. space units
Hence comma space correct space option space is space left parenthesis straight d right parenthesis. end style

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