Chapter 5 : Coordinate Geometry - R S Aggarwal And V Aggarwal Solutions for Class 9 Maths CBSE

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Chapter 5 - Coordinate Geometry Excercise 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

If x > 0 and y

(a) Quadrant I

(b) Quadrant III

(c) Quadrant II

(d) Quadrant IV

Solution 2

Correct option: (d)

  

Question 3

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 3

Correct option: (b)

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

Question 4

A point both of whose coordinates are negative lies in

(a) Quadrant I

(b) Quadrant II

(c) Quadrant III

(d) Quadrant IV

Solution 4

Correct option: (c)

  

  

Question 5

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

Solution 5

Correct option: (c)

  

  

Question 6

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

Solution 6

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 7

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 7

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 8

Point (0, -8) lies

(a) in the II quadrant

(b) in the IV quadrant

(c) on the x-axis

(d) on the y-axis

Solution 8

Correct option: (d)

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

Question 9

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

Solution 9

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. 

Question 10

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 10

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 11

The ordinate of every point on the x-axis is

(a) 1

(b) -1

(c) 0

(d) any real number

Solution 11

Correct option: (c)

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

Question 12

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

Solution 12

Correct option: (b)

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

Question 13

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 13

Correct option: (b)

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

  

Question 14

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 14

Correct option: (b)

Abscissa of A - Abscissa of B

= -2 - (-3)

= -2 + 3

= 1 

Question 15

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

(a) 3

(b) 4

(c) 5

(d) 7

Solution 15

Correct option: (a)

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

Question 16

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

Solution 16

Correct option: (b)

  

  

Question 17

The point at which the two coordinate axes meet is called

(a) The abscissa

(b) The ordinate

(c) The origin

(d) The quadrant

Solution 17

  

Question 18

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 18

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 19

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 19

  

Question 20

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 20

  

Question 21

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

(a) (3, -6)

(b) (-3, 4)

(c) (5, 7)

(d) (0, 3)

Solution 21

Correct option: (d)

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

Question 22

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 22

Correct option: (c)

  

Clearly, ΔAOB is a right-angled triangle.

Chapter 5 - Coordinate Geometry Excercise 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

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