Maths MCQ Ch-7 Class 10 | Co-ordinate Geometry

Mathematics

Multiple Choice Questions (MCQ)
MCQ | Class 10 | Chapter 7 
Co-ordinate Geometry

Q 1) The distance of the point P(2, 3) from the x-axis is
(a) 2
(b) 3
(c) 1
(d) 5 

Ans: b

Q 2) The distance between the point P(1, 4) and Q(4, 0) is
(a) 4
(b) 6
(c) 5
(d) 3√3 

Ans: c

Q 3) Point of intersection of x – axis and y – axis is
a) (x, y)
b) (0, 0)
c) (x, 0)
d) (0, y) 

 Ans: b

Q 4) Find the distance between (-3, 0) and (5, 0)
a) 8
b) 2
c) -2
d) -8 

Ans: a

Q 5) Any point on the x - axis is of the form
a) (0, x)
b) (x, y)
c) (y, 0)
d) (x, x) 

 Ans: c

Q 6) Any point on the y - axis is of the form
a) (0, x)
b) (x, y)
c) (y, 0)
d) (y, y) 

 Ans: a

Q 7) Find the distance between (0, 3) and (0, -4)
a) -1
b) 1
c) 7
d) -7 

Ans: c

Q 8) Find the distance of (-2, 4) from y – axis
a) -2
b) 2
c) 4
d) -4 

Ans: b

Q 9) Find the distance of (4, -5) from x – axis
a) -5
b) 4
c) -4
d) 5 

Ans: d

Q 10) Find the distance of (-3, 2) from origin
a) 3
b) 2

 

Ans: c

Q 11) Find the distance between (1, 4) and (2, 3)

  b)     2

 

Ans: 

a) 5
b) 25

d) 10 

Ans a

Q 13) Find the distance between (-a, b), and (a, -b)
  (a)    2(a + b)


 

Ans: c

Q 14) Find y for which the distance between the points (2, -3) and (10, y) is 10
a) -3, 9
b) 3, 9
c) - 3, - 9
d) 3, -9
Ans: d

Q 15) If the point (2, -4) is equidistant from points (3, 8) and (-10, y), find y
a) -3
b) -5
c) -3, -5
d) -3, 5 

Ans: c

Q 16) The perimeter of the triangle with vertices (3, 0), (0, 4) and (0, 0) is
  a)    7
  b)   12

  d)   8 

Ans: b

Q 17) If point (x, y) is equidistant from(2, 5) and (-3, 7) then
a) 10x - 4y = 29
b) 10x + 4y = 29
c) -10x + 4y = - 29
d) 10x – 4y = - 29 

Ans: d

Q 18) The line 3x + y – 9 = 0 divides the line joining the points (1, 3) and (2, 7) internally in the ratio
(a) 3 : 4
(b) 3 : 2
(c) 2 : 3
(d) 4 : 3 

Ans: a

Q 19) If (a / 3, 4) is the mid-point of the segment joining the points P(-6, 5) and R(-2, 3), then the value of ‘a’ is
(a) 12
(b) - 6
(c) -12
(d) – 4 

Ans: c

Q 20) If the distance between the points (x, -1) and (3, 2) is 5, then the value of x is
(a) -7 or -1
(b) -7 or 1
(c) 7 or 1
(d) 7 or -1
Ans: d

Explanation

Squaring on both side we get⇒ (x – 3)² + 9 = 25
⇒ x² – 6x + 9 + 9 = 25
⇒ x² -6x – 7 = 0 ⇒ (x – 7)(x + 1) = 0
⇒ x = 7 or x = -1

Q 21) The fourth vertex D of a parallelogram ABCD whose three vertices are A(-2, 3), B(6, 7) and C(8, 3) is
(a) (0, 1)
(b) (0, -1)
(c) (-1, 0)
(d)(1, 0)

Ans: b

Q 22) The points (1,1), (-2, 7) and (3, -3) are
(a) vertices of an equilateral triangle
(b) collinear
(c) vertices of an isosceles triangle
(d) none of these
Ans: b

Explanation
Let A(1,1), B(-2, 7) and C(3,3) are the given points, then we have



Clearly BC = AB + AC
Therefore A, B, C are collinear

Q 23) The coordinates of the centroid of a triangle whose vertices are (0, 6), (8,12) and (8, 0) is
(a) (4, 6)
(b) (16, 6)
(c) (8, 6)
(d) (16/3, 6)
Ans: d

Explanation:
The coordinates of the centroid of the triangle is

Q 24) Two vertices of a triangle are (3, – 5) and (- 7, 4). If its centroid is (2, -1), then the third vertex is
(a) (10, 2)
(b) (-10,2)
(c) (10,-2)
(d) (-10,-2)
Ans: c

Explanation
Let the coordinates of the third vertex is (x, y), then



⇒ x = 6 + 4 and y = -3 + 1
⇒ x = 10 and y = -2
Coordinates of third vertex is (10, -2)

Q 25) If the distance between the points (4, P) and (1, 0) is 5, then the value of P is
(a) 4 only
(b) ± 4
(c) -4 only
(d) 0
Ans: b

Q 26) The points (- 4, 0), (4, 0), (0, 3) are the vertices of a
a) Right Triangle
b) Isosceles Triangle
c) Equilateral Triangle
d) Scalene Triangle 

Ans: b

Q 27) The distance of the point P(- 6, 8) from the origin is
 a)    8

 c)   10
 d)   6 

Ans: c

Q 28) The points (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0) forms a quadrilateral of type:
(a) Square
(b) Rectangle
(c) Parallelogram
(d) Rhombus 

Ans: a

Q 29) If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then the value of x is:
(a) 1
(b) -2
(c) 2
(d) -1 

Ans: c

Q 30) The midpoints of a line segment joining two points A(2, 4) and B(-2, -4)
(a) (-2,4)
(b) (2,-4)
(c) (0, 0)
(d) (-2,-4) 

Ans: c

Q 31) The distance of point A(2, 4) from x-axis is

(a) 2 units                   

(b) - 4 units                       

(c) -2 units                        

(d) 4 units

Ans:  d

Q 32)  The distance between the points P(0, 2) and Q(6, 0) is

(a) 4√10                     

(b) 2√10                             

(c) √10                              

(d) 20

Ans:  b

Q 33) The point which divides the line segment of points P(-1, 7) and (4, -3) in the ratio of 2:3 is:

(a) (-1, 3)                      

(b) (-1, -3)                      

(c) (1, -3)                      

(d) (1, 3)

Ans:  d

Q 34) The ratio in which the line segment joining the points P(-3, 10) and Q(6, – 8) is divided by O(-1, 6) is:

(a) 1:3                  

(b) 3:4                          

(c) 2:7                        

(d) 2:5

Ans:  c

Q 35) The coordinates of a point P, where PQ is the diameter of a circle whose centre is (2, – 3) and Q is (1, 4) is:

(a) (3, -10)                  

(b) (2, -10)                        

(c) (-3, 10)                       

(d) (-2, 10)

Ans:  a 

Q 36) The area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2,-1) taken in order, is:

(a) 12 sq. units  

(b) 24 sq. units 

(c) 30 sq. units

(d) 32 sq. units

Ans: b

Q 37) The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is

(a) 5                           

(b) 11                             

(c) 12                            

(d) 7

Ans: c 

Q 38) If the points A(6, 1), B(8, 2), C(9, 4) and D (p, 3) are the vertices of a parallelogram, taken in order, then the value of p is

(a)  4                      

(b) - 6                          

(c)  7                         

(d) – 2

Ans: c 

Q 39)  If the point P(p, q) is equidistant from the points A(a + b, b – a) and  B(a – b, a + b), then

a) ap = by                                                        

b) bp = aq

c) ap + bq = 0                                                

d) bp + aq = 0

Ans: b 

Q 40)  The point which divides the line joining the points A(1, 2) and B(- 1, 1) internally in the ratio 1 : 2 is

  

c) (- 1, 5)                                                           

d) (1, 5)

Ans: b 

Q 41) Ratio in which the line  3x + 4y = 7 divides the line segment joining the points (1, 2) and (- 2, 1) is

a)  3 : 5    

b) 4 : 6   

c) 4 : 9  

d) None of these

Ans: c

Q 42) If (x, y) is equidistant from (7, 1) and (3, 5) then

a)  x + y = 2 

b) x – y = -2

c) x + y + 2 = 0 

d) x – y = 2

Ans: d 

Q 43) If (-1, -2), (1, 0), (-1, 2) and (-3, 0) forms a square then its perimeter is

a) 8

b) 4 

c) 2

d) 8

Ans: a 

Q 44) If AB is the diameter of the circle with centre O, find point B if A and O are (4, -1) and (1, -3) respectively.

a) (2, -5)  

b) (-2, 5)  

c) (-2, -5)

d) (2, 5)

Ans: c

Q 45)  In what ratio does the x-axis divide the join of  (2, -4) and (-3, 6)

a)  3 : 2 

b) 2 : 3

c) 3 : 4

d) 4 : 3

Ans: b 

Q 46)  In what ratio does the y-axis divide the join of  (5, -6) and (-1, -4)

a)  5 : 1     

b) 2 : 3  

c) 3 : 4 

d) 1 : 5

Ans: a 

Q 47)  Three vertices of a parallelogram taken in order are (1, -2), (3, 6) and  (5, 10). Find the fourth vertex.

a) (2, 3) 

b) (3, 4)

c) (3, 2) 

d) (4, 3)

Ans: c 

Q 48)  If the points (x, -11), (5, y), (2, 15) and (1, 1) are the vertices of a rhombus , taken in order , find x and y.

a)  3, 4 

b)  4, 3

c)  5, 8

d) 7, 4

Ans:  b 

Q 49) The point which divides the line segment joining (-2, 3) and (1, -2) in 1 : 2 internally, lies in the quadrant

a)  I   

b)  II  

c)  III

d)  IV

Ans: b

Q 50)  The perpendicular bisector of the line segment joining the points A(2, 4) and B(4, 6) meet the line AB at

a)  (0, 13)  

b) (0, - 13) 

c) (0, 12)

d) (3, 5)

Ans: d 

Questions from CBSE Sample Paper
And From CBSE Board Exam

Q 51)  The co-ordinates of the point P dividing the line segment joining the points A (1,3) and B (4,6)  internally in the ratio 2 : 1 are

(a) (2,4)

(b) (4,6)

(c) (4,2) 

(d) (3,5)

Ans: d

Q 52) The mid-point of (3p, 4) and (-2, 2q) is (2,6) . Find the value of p + q

(a) 5  

(b) 6

(c) 7  

(d) 8

Ans: b

Q 53)  The vertices of a parallelogram in order are A(1,2), B(4, y), C(x, 6) and D(3,5). Then (x, y) is

(a) (6, 3) 

(b) (3, 6)

(c) (5, 6)

(d) (1, 4)

Ans: a

Q 54) Point P divides the line segment joining R(-1, 3) and S(9,8) in ratio k :1. If P lies on the line x – y + 2 = 0, then value of k is

(a) 2/3

(b) 1/2

(c) 1/3

(d) 1/4

Ans: a 

Q 55) Given below is the graph representing two linear equations by lines AB and CD respectively. What is the area of the triangle formed by these two lines and the line x = 0?

(a) 3sq. units 

(b) 4sq. units

(c) 6sq. units  

(d) 8sq. units

Ans: c 

Q 56)  The distance between the points A(0, 6) and B(0, -2) is :

a)  6 units   

b)  8 units   

c)  4 units         

d) 2 units

Ans: b

Q 57)  The point on the x-axis equidistant from the points P(5, 0) and Q(-1, 0) is :

a)  (2, 0) 

b)  (-2, 0) 

c)  (3, 0) 

d)  (2, 2)

Ans: c

Q 58) The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from Q(2, -5) and R(-3, 6), then the coordinates of point P are :

a)  (8, 16)   

b)  (10, 20)  

c) (20, 10)     

d)  (16, 8)

Ans: d 

Q 59) If the point (x, 4) lies on the circle  whose centre is at the origin and radius is 5 cm, then the value of x is :

a)  0  

b)  土 4  

c)  土 5

d)  土 3

Ans: d

Q 60)  The ratio in which the point (-4, 6) divides the line segment joining the points A(-6, 10) and B (3, -8) is :

a)  2 : 5         

b)  7 : 2             

c) 2 : 7       

d) 5 : 2

Ans: c

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