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

## Chapter 5 – Coordinate Geometry Exercise Ex. 5

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)

The

given points are plotted as follows:

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

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)

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)

(i) (-6, 3):

x co-ordinate

is negative and y co-ordinate is positive.

Hence, (-6, 3) lies

in the 2^{nd} Quadrant.

(ii) (-5, -3) :

x co-ordinate

and y co-ordinate both are negative.

Hence, (-5, -3)

lies in the 3^{rd} Quadrant.

(iii) (11, 6):

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

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

(iv) (1, -4):

x co-ordinate

is positive and y co-ordinate is negative.

Hence, (1, -4) lies in the 4^{th}

Quadrant.

(v) (-7, -4):

x co-ordinate

and y co-ordinate both are negative.

Hence, (-7, -4)

lies in the 3^{rd} Quadrant.

(vi) (4, -1):

x co-ordinate

is positive and y co-ordinate is negative.

Hence, (4, -1)

lies in the 4^{th} Quadrant.

(vii) (-3, 8):

x co-ordinate

is negative and y co-ordinate is positive.

Hence, (-3, 8)

lies in the 2^{nd} Quadrant.

(viii) (3, -8):

x

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

Hence, (3, -8)

lies in the 4^{th} Quadrant.

Write the axis on which the given point lies.

(i) (2, 0) (ii) (0,

-5) (iii) (-4, 0) (iv) (0, -1)

(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).

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)

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)

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.

The

given points are plotted on the graph paper as follows:

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).

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

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

(a) IV

(b) II

(c) III

(d) None

of these

Correct

option: (c)

Since,

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

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)

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).

The ordinate of every point on the x-axis is

(a) 1

(b) -1

(c) 0

(d) any

real number

Correct

option: (c)

The ordinate (y co-ordinate) of

every point on the x-axis is 0.

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

always lies

(a) on

the y-axis

(b) on

the x-axis

(c) in

the I quadrant

(d) in

the IV quadrant

Correct

option: (b)

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

always lies on the x-axis.

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

Correct

option: (b)

By

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

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

Correct

option: (b)

Abscissa of A – Abscissa of B

= -2 – (-3)

= -2 + 3

= 1

The perpendicular distance of the point A(3, 4) from the

y-axis is

(a) 3

(b) 4

(c) 5

(d) 7

Correct

option: (a)

The perpendicular distance of the point A(3,

4) from the y-axis is 3 units.

Abscissa of a point is positive in

(a) I and II quadrants

(b) I and IV quadrants

(c) I quadrant only

(d) II quadrant only

Correct option: (b)

The point at which the

two coordinate axes meet is called

(a) The abscissa

(b) The ordinate

(c) The origin

(d) The quadrant

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)

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).

Which of the following

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

(a) (2,8)

(b) (3,9)

(c) (4,12)

(d) (5,15)

If x > 0 and y

(a) Quadrant I

(b) Quadrant III

(c) Quadrant II

(d) Quadrant IV

Correct option: (d)

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)

Which of the following points does not lie in any

quadrant?

(a) (3,

-6)

(b) (-3, 4)

(c) (5,

7)

(d) (0, 3)

Correct

option: (d)

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

y-axis.

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

Correct

option: (c)

Clearly, ΔAOB

is a right-angled triangle.

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

quadrant

(a) IV

(b) II

(c) III

(d) none of these

Correct

option: (b)

Since,

x co-ordinate is negative and y co-ordinate is positive, the given point lies

in Quadrant II.

A point both of whose

coordinates are negative lies in

(a) Quadrant I

(b) Quadrant II

(c) Quadrant III

(d) Quadrant IV

Correct

option: (c)

The points (other than

the origin) for which the abscissa is equal to the ordinate lie in

(a) Quadrant I only

(b) Quadrants I and

II

(c) Quadrants I and

III

(d) Quadrants II

and IV

Correct

option: (c)

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

(a) same

quadrant

(b) II

and III quadrants respectively

(c) II

and IV quadrants respectively

(d) IV

and II quadrants respectively

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.

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

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.

Point (0, -8) lies

(a) in

the II quadrant

(b) in

the IV quadrant

(c) on

the x-axis

(d) on

the y-axis

Correct

option: (d)

Point

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

Point (-7, 0) lies

(a) on

the negative direction of the x-axis

(b) on

the negative direction of the y-axis

(c) in

the III quadrant

(d) in

the IV quadrant

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.