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

## 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.

If x > 0 and y

(a) Quadrant I

(b) Quadrant III

(c) Quadrant II

(d) Quadrant IV

Correct option: (d)

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.

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)

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.

## 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

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