# R S AGGARWAL AND V AGGARWAL Solutions for Class 9 Maths Chapter 5 - Coordinate Geometry

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## Chapter 5 - Coordinate Geometry Exercise Ex. 5

Question 1

On the plane of a graph paper draw X'OX and YOY' as coordinate axes and plot each of the following points.

(i) A(5, 3) (ii) B(6, 2) (iii) C(-5, 3) (iv) D(4, -6)

(v) E(-3, -2) (vi) F(-4, 4) (vii) G(3, -4) (viii) H(5, 0)

(ix) I(0, 6) (x) J(-3, 0) (xi) K(0, -2) (xii) O(0, 0)

Solution 1

The given points are plotted as follows: Question 2

Write down the coordinates of each of the points A, B, C, D, E shown below: Solution 2

Draw the perpendiculars from the AF, BG, CH, DI and EJ on the x-axis.

(1) The distance of A from the y-axis = OF = -6 units

The distance of A from the x-axis = AF = 5 units

Hence, the coordinate of A are (-6, 5)

(2)The distance of B from the y-axis = OG = 5 units

The distance of B from the x-axis = BG = 4 units

Hence, the coordinate of B are (5, 4)

(3)The distance of C from the y-axis = OH = -3 units

The distance of C from the x-axis = HC = 2 units

Hence, the coordinate of C are (-3, 2)

(4)The distance of D from the y-axis = OI = 2 units

The distance of D from the x-axis = ID = -2 units

Hence, the coordinate of D are (2, -2)

(5)The distance of E from the y-axis = OJ = -1 unit

The distance of E from the x-axis = JE = -4 units

Hence, the coordinate of E are (-1, -4)

Thus, the coordinates of A, B, C, D and E are respectively, A(-6,5), B(5,4), C(-3,2), D(2,-2) and E(-1,-4)

Question 3

For each of the following points, write the quadrant in which it lies.

(i) (-6, 3) (ii) (-5, -3) (iii) (11, 6) (iv) (1, -4)

(v) (-7, -4) (vi) (4, -1) (vii) (-3, 8) (viii) (3, -8)

Solution 3

(i) (-6, 3):

x co-ordinate is negative and y co-ordinate is positive.

Hence, (-6, 3) lies in the 2nd Quadrant.

(ii) (-5, -3) :

x co-ordinate and y co-ordinate both are negative.

Hence, (-5, -3) lies in the 3rd Quadrant.

(iii) (11, 6):

x co-ordinate and y co-ordinate both are positive.

Hence, (11, 6) lies in the 1st Quadrant.

(iv) (1, -4):

x co-ordinate is positive and y co-ordinate is negative.

Hence, (1, -4) lies in the 4th Quadrant.

(v) (-7, -4):

x co-ordinate and y co-ordinate both are negative.

Hence, (-7, -4) lies in the 3rd Quadrant.

(vi) (4, -1):

x co-ordinate is positive and y co-ordinate is negative.

Hence, (4, -1) lies in the 4th Quadrant.

(vii) (-3, 8):

x co-ordinate is negative and y co-ordinate is positive.

Hence, (-3, 8) lies in the 2nd Quadrant.

(viii) (3, -8):

x co-ordinate is positive and y co-ordinate is negative.

Hence, (3, -8) lies in the 4th Quadrant.

Question 4

Write the axis on which the given point lies.

(i) (2, 0) (ii) (0, -5) (iii) (-4, 0) (iv) (0, -1)

Solution 4

(i) (2, 0) lies on the x-axis as the co-ordinates of every point on the x-axis are of the form (x, 0).

(ii) (0, -5) lies on the y-axis as the co-ordinates of every point on the y-axis are of the form (0, y).

(iii) (-4, 0) lies on the x-axis as the co-ordinates of every point on the x-axis are of the form (x, 0).

(iv) (0, -1) lies on the y-axis as the co-ordinates of every point on the y-axis are of the form (0, y).

Question 5

Which of the following points lies on the x-axis?

(i) A(0, 8) (ii) B(4, 0) (iii) C(0, -3) (iv) D(-6, 0)

(v) E(2, 1)  (vi) F(-2, -1) (vii) G(-1, 0) (viii) H(0, -2)

Solution 5

The co-ordinates of every point on the X-axis are of the form (x, 0).

Hence, following points lie on the x-axis:

(ii) B(4, 0)

(iv) D(-6, 0)

(vii) G(-1, 0)

Question 6

Plot the points A(2,5), B(-2, 2) and C(4, 2) on a graph paper. Join AB, BC and AC. Calculate the area of ΔABC.

Solution 6

The given points are plotted on the graph paper as follows:  Question 7

Three vertices of a rectangle ABCD are A(3, 1), B(-3, 1) and C(-3, 3). Plot these points on graph paper and find the coordinates of the fourth vertex D. Also, find the area of rectangle ABCD.

HINT Coordinates of D are (3, 3).

Solution 7

The given vertices of rectangle ABCD are plotted on graph paper as follows: The coordinates of fourth vertex D are (3, 3)

Area of rectangle ABCD = Length × Breadth

= AB × BC

= 6 × 2

= 12 square units

## Chapter 5 - Coordinate Geometry Exercise MCQ

Question 1

In which quadrant does the point (-7, -4) lie?

(a) IV

(b) II

(c) III

(d) None of these

Solution 1

Correct option: (c)

Since, both the coordinates of given point are negative, it lies in Quadrant III.

Question 2

The point which lies on the y-axis at a distance of 5 units in the negative direction of the y-axis is

(a) (-5, 0)

(b) (0, -5)

(c) (5, 0)

(d) (0, 5)

Solution 2

Correct option: (b)

The point which lies on the y-axis at a distance of 5 units in the negative direction of the y-axis is (0, -5).

Question 3

The ordinate of every point on the x-axis is

(a) 1

(b) -1

(c) 0

(d) any real number

Solution 3

Correct option: (c)

The ordinate (y co-ordinate) of every point on the x-axis is 0.

Question 4

If the y-coordinate of a point is zero then this point always lies

(a) on the y-axis

(b) on the x-axis

Solution 4

Correct option: (b)

If the y-coordinate of a point is zero then this point always lies on the x-axis.

Question 5

If O(0,0), A(3, 0), B(3, 4), C(0, 4) are four given points then the figure OABC is a

(a) square

(b) rectangle

(c) trapezium

(d) rhombus

Solution 5

Correct option: (b)

By plotting the given points, we find that figure OABC is a rectangle. Question 6

If A(-2, 3) and B(-3, 5) are two given points then (abscissa of A) - (abscissa of B) = ?

(a) -2

(b) 1

(c) -1

(d) 2

Solution 6

Correct option: (b)

Abscissa of A - Abscissa of B

= -2 - (-3)

= -2 + 3

= 1

Question 7

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

(a) 3

(b) 4

(c) 5

(d) 7

Solution 7

Correct option: (a)

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

Question 8

Abscissa of a point is positive in

Solution 8

Correct option: (b)  Question 9

The point at which the two coordinate axes meet is called

(a) The abscissa

(b) The ordinate

(c) The origin

Solution 9 Question 10

The point whose ordinate is 3 and which lies on the y-axis is

(a) (3, 0)

(b) (0, 3)

(c) (3, 3)

(d) (1, 3)

Solution 10

Correct option: (b)

If a point lies on y-axis, then its abscissa is 0.

Hence, the point whose ordinate is 3 and which lies on the y-axis is (0, 3).

Question 11

Which of the following points lies on the line y = 2x + 3?

(a) (2,8)

(b) (3,9)

(c) (4,12)

(d) (5,15)

Solution 11 Question 12

If x > 0 and y

Solution 12

Correct option: (d)  Question 13

Which of the following points does not lie on the line y = 3x + 4?

(a) (1,7)

(b) (2,10)

(c) (-1,1)

(d) (4,12)

Solution 13 Question 14

Which of the following points does not lie in any quadrant?

(a) (3, -6)

(b) (-3, 4)

(c) (5, 7)

(d) (0, 3)

Solution 14

Correct option: (d)

The abscissa of point (0, 3) is 0. Hence, it lies on y-axis.

Question 15

The area of ΔAOB having vertices A(0,6), O(0,0) and B(6, 0) is

(a) 12 sq units

(b) 36 sq units

(c) 18 sq units

(d) 24 sq units

Solution 15

Correct option: (c) Clearly, ΔAOB is a right-angled triangle. Question 16

If a < 0 and b > 0 then the point (a, b) lies in quadrant

(a) IV

(b) II

(c) III

(d) none of these

Solution 16

Correct option: (b)

Since, x co-ordinate is negative and y co-ordinate is positive, the given point lies in Quadrant II.

Question 17

A point both of whose coordinates are negative lies in

Solution 17

Correct option: (c)  Question 18

The points (other than the origin) for which the abscissa is equal to the ordinate lie in

Solution 18

Correct option: (c)  Question 19

The point (-5, 3) and (3, -5) lie in the

(b) II and III quadrants respectively

(c) II and IV quadrants respectively

(d) IV and II quadrants respectively

Solution 19

Correct option: (c)

For point (-5, 3), the x co-ordinate is negative and the y co-ordinate is positive. Hence, it lies in Quadrant II.

For point (3, -5), the x co-ordinate is positive and the y co-ordinate is negative. Hence, it lies in Quadrant IV.

Question 20

Points (1, -1), (2, -2), (-3, -4), (4, -5)

(a) all lie in the II quadrant

(b) all lie in the III quadrant

(c) all lie in the IV quadrant

(d) do not lie in the same quadrant

Solution 20

Correct option: (d)

Points (1, -1), (2, -2) and (4, -5) lie in Quadrant IV, but point (-3, -4) lies in Quadrant III.

Hence, all the given points do not lie in the same quadrant.

Question 21

Point (0, -8) lies

(c) on the x-axis

(d) on the y-axis

Solution 21

Correct option: (d)

Point (0, -8) lies on y-axis as its x co-ordinate is 0.

Question 22

Point (-7, 0) lies

(a) on the negative direction of the x-axis

(b) on the negative direction of the y-axis

Solution 22

Correct option: (a)

Point (-7, 0) lies on negative direction of the x-axis as its x co-ordinate is negative and y co-ordinate is zero.