# MCQs for Class 10 Maths Chapter 7 Coordinate Geometry

MCQs for Class 10 Maths Chapter 7 Co-Ordinate Geometry: In this article, we have covered all the important MCQs for Free for Class 10 Term 1 2021-22 Board Exams. In accordance with the latest pattern, Padhle is here with MCQ Questions for Class 10.

# MCQs for Class 10 Maths Chapter 7 Co-Ordinate Geometry

1. The distance of the point P(2, 3) from the x-axis is

(a) 2

(b) 3

(c) 1

(d) 5

2.  If the distance between the points (2, –2) and (–1, x) is 5, one of the values of x is

(a) –2

(b) 2

(c) –1

(d) 1

3. The points (- 1, – 2), (1, 0), (- 1, 2), (- 3, 0) forms a quadrilateral of type:

(a)Square

(b)Rectangle

(c)Parallelogram

(d)Rhombus

4. The distance between the points A(0, 6) and B(0, -2) is

(a) 6

(b) 8

(c) 4

(d) 2

5.The distance between the point P(1, 4) and Q(4, 0) is

(a) 4

(b) 5

(c) 6

(d) 3√3

6. Find the coordinates of the point equidistant from the points A(1, 2), B (3, –4) and C(5, –6).

(a) (2, 3)

(b) (–1, –2)

(c) (0, 3)

(d) (1, 3)

7. The area of triangle whose vertices are (1,-1), (-4.6), and (-3, -5) is

(a) 21

(b) 32

(c) 24

(d) 25

8. The points (-5, 1), (1, p) and (4, -2) are collinear if the value of p is

(a) 3

(b) 2

(c) 1

(d) -1

9. The distance between the point P(1, 4) and Q(4, 0) is

(a) 4

(b) 5

(c) 6

(d) 3√3

10. The mid-point of the line segment joining the points A (–2, 8) and B (– 6, – 4) is

(a) (– 4, – 6)

(b) (2, 6)

(c) (– 4, 2)

(d) (4, 2)

11. 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)

12. The distance of the point P(-6, 8) from the origin is

(a) 8

(b) 2√7

(c) 10

(d) 6

13.  The area of the triangle whose vertices are A(1, 2), B(-2, 3) and C(-3, -4) is

(a) 11

(b) 22

(c) 33

(d) 21

14.  Find the coordinates of the point equidistant from the points A(5, 1), B(–3, –7) and C(7, –1).

(a) (2, –4)

(b) (3, –6)

(c) (4, 7)

(d) (8, –6)

15.  If the area of a quadrilateral ABCD is zero, then the four points A, B, C, D are

(a) Collinear

(b) Not collinear

(c) Nothing can be said

(d) None of these

16. The area of the triangle ABC with the vertices A(-5, 7), B(-4, -5) and C(4, 5) is

(a) 63

(b) 35

(c) 53

(d) 36

17. The points (-5, 1), (1, p) and (4, -2) are collinear if the value of p is

(a) 3

(b) 2

(c) 1

(d) -1

18. The points A (9, 0), B (9, 6), C (–9, 6) and D (–9, 0) are the vertices of a

(a) Square

(b) Rectangle

(c) Rhombus

(d) Trapezium

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

(a)4√10

(b)2√10

(c)√10

(d)20

20. The distance between the points (0, 5) and (-5, 0) is

(a) 5

(b) 5√2

(c) 2√5

(d) 10

21. The coordinates of the centre of a circle passing through (1, 2), (3, – 4) and (5, – 6) is:​

(a) (11, – 2)

(b) (-2, 11)

(c) (11, 2)

(d) (2, 11)

22. Find the value of P for which the point (–1, 3), (2, p) and (5, –1) are collinear.

(a) 4

(b) 3

(c) 2

(d) 1

23.  If (1,2), (4,y), (x,6), and (3,5) are the vertices of a parallelogram taken in order. Then (x,y) is

(a) (6, 2)

(b) (6, 3)

(c) (6, 4)

(d) (3, 4)

24.  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

25.  The area of the triangle ABC with the vertices A(-5, 7), B(-4, -5) and C(4, 5) is

(a) 63

(b) 35

(c) 53

(d) 36

26. The distance of the point P (2, 3) from the x-axis is

(a) 2

(b) 3

(c) 1

(d) 5

27. .If O(p/3, 4) is the midpoint of the line segment joining the points P(-6, 5) and Q(-2, 3). The value of p is:

(a)7/2

(b)-12

(c)4

(d)-4

28. AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is

(a) 5

(b) 3

(c) √34

(d) 4

29. The distance of the point (– 3, 4) from the origin is

(a) 25 units

(b) 1 unit

(c) 7 units

(d) 5 units

30. Find the distance of the point (–6, 8) from the origin.

(a) 8

(b) 11

(c) 10

(d) 9

31. The coordinates of a point A, where AB is the diameters of a circle whose centre (2,-3) and B is (1,4) is

(a) (3, -9)

(b) (2, 9)

(c) (3, -10)

(d) (4, 5)

32. The area of the triangle formed by the points A(-1.5, 3), B(6, -2) and C(-3, 4) is

(a) 0

(b) 1

(c) 2

(d) 3/2

33. The distance of the point (α, β) from the origin is

(a) α + β

(b) α² + β²

(c) |α| + |β|

(d) √(α22)

34. The distance between the points A (0, 6) and B (0, –2) is

(a) 6

(b) 8

(c) 4

(d) 2

35. The points 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)

36. The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is

(a) 5

(b) 12

(c) 11

(d) 7 + √5

37.  The distance of the point P (2, 3) from the x-axis is

(a) 2

(b) 3

(c) 1

(d) 5

38.  Find the value of p for which the points (–5, 1), (1, p) and (4, –2) are collinear.

(a) –3

(b) –2

(c) 0

(d) –1

39. Let P(x, y) be equidistant from the points A (7, 1) and (3, 5).Find a relation between x and y.​

(a) y – x = 4

(b) y – x = 2

(c) x – y = 2

(d) x – y = 4

Answer: (c) x – y = 2

40.  If the points P(1, 2), B(0, 0) and C(a, b) are collinear, then

(a) 2a = b

(b) a = -b

(c) a = 2b

(d) a = b

41. The line segment joining the points (3, -1) and (-6, 5) is trisected. The coordinates of point of trisection are

(a) (3, 3)

(b) (- 3, 3)

(c) (3, – 3)

(d) (-3,-3)

42. If P (a/3, 4) is the mid-point of the line segment joining the points Q (– 6, 5) and R (– 2, 3), then the value of a is

(a) – 4

(b) – 12

(c) 12

(d) – 6

43. 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

44. The area of a triangle with vertices A(3, 0), B(7, 0) and C(8, 4) is

(a) 14

(b) 28

(c) 8

(d) 6

45. The distance between the points (a, a) and (−√3a,√3a) is

(a) 3√2a units

(b) 2√2a units

(c) 2√2 units

(d) 2 units

46.  Find the value of k if the points A(2, 3), B(4, k) and C(6, –3) are collinear.

(a) 2

(b) 3

(c) 0

(d) 1

47. The coordinates of the point which divides the line segment joining points A(5,-2) and B(9,6) in the ratio 3:1 are​

(a) (-4,3)

(b) (5,-6)

(c) (8,4)

(d) (0,7)

48. If the segment joining the points (a, b) and (c, d) subtends a right angle at the origin, then

(a) ac – bd = 0

(b) ac + bd = 0

(c) ab + cd = 0

(d) ab – cd= 0

Answer: (b) ac + bd = 0

49. 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

50. 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

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

(a)(3, -10)

(b)(2, -10)

(c)(-3, 10)

(d)(-2, 10)

52. The points (-4, 0), (4, 0), (0, 3) are the vertices of a

(а) Right triangle

(b) Isosceles triangle

(c) Equilateral triangle

(d) Scalene triangle

53. The mid-point of the line segment joining the points A (-2, 8) and B (-6, -4) is

(a) (-4, -6)

(b) (2, 6)

(c) (-4, 2)

(d) (4, 2)

54.  In what ratio of line x – y – 2 = 0 divides the line segment joining (3, –1) and (8, 9)?

(a) 1 : 2

(b) 2 : 1

(c) 2 : 3

(d) 1 : 3

55. The co-ordinates of the points which divides the join of (– 2, – 2) and (– 5, 7) in the ratio 2 : 1 is :

(a) (4, – 4)

(b) (– 3, 1)

(c) (– 4, 4)

(d) (1, – 3)

56. 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

57. The point which divides the line segment joining the points (7, –6) and (3, 4) in ratio 1 : 2 internally lies in the

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

(a)12 sq.unit

(b)24 sq.unit

(c)30 sq.unit

(d)32 sq.unit

59. 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)

60. The area of the triangle formed by joining the mid-points of the sides of the triangle, whose vertices are (0, -1), (2, 1) and (0, 3) is

(a) 4

(b) 2

(c) 3

(d) 1

61. The vertices of a ΔABC and given by A(2, 3) and B(–2, 1) and its centroid is G (1 ½)      Find the coordinates of the third vertex C of the ΔABC.

(a) (0, 2)

(b) (1, –2)

(c) (2, –3)

(d) (–2, 3)

62. The distance between the points P (-6,7) and Q (-1,-5) is​

(a) 15

(b) 12

(c) 13

(d) 10

63.  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)

64. One of the two points of trisection of the line segment joining the points A (7, – 2) and B (1, – 5) which divides the line in the ratio 1:2 are:

(a) (5, –3)

(b) (5, 3)

(c) (–5, –3)

(d) (13, 0)

65. If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then

(a) AP = 1/3 AB

(b) AP = PB

(c) PB = 1/3 AB

(d) AP = 1/2 AB

Answer: (d) AP = 1/2 AB

66. The ordinate of a point is twice its abscissa. If its distance from the point (4,3) is √10,  then the coordinates of the point are​

(a) (1,2) or (3,6)

(b) (1,2) or (3,5)

(c) (2,1) or (3,6)

(d) (2,1) or (6,3)

67. Find the ratio in which the line joining the points (6, 4) and (1, –7) is divided by x-axis.

(a) 1 : 3

(b) 2 : 7

(c) 4 : 7

(d) 6 : 7

68. The coordinates of the centre of a circle are (– 6, 1.5). If the ends of a diameter are (– 3, y) and (x, – 2) then:

(a) x = – 9, y = 5

(b) x = 5, y = – 9

(c) x = 9, y = 5

(d) None of these

Answer: (a) x = – 9, y = 5

69. 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)

70. A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, –5) is the mid – point of PQ, then the coordinates of P and Q are, respectively.

(a) (0, – 5) and (2, 0)

(b) (0, 10) and (– 4, 0)

(c) (0, 4) and (– 10, 0)

(d) (0, – 10) and (4, 0)

Answer:  (d) (0, – 10) and (4, 0)

71. If P (α3, 4) is the mid-point of the line segment joining the points Q(-6, 5) and R(-2, 3), then the value of‘a’ is

(a) -4

(b) -12

(c) 12

(d) -6

72. If (a, 0) , (0, b) and (x, y) are collinear, then

(a) ay + bx = ab

(b) ax + by = 1

(c) ax – by = ab

(d) ay – bx = 1

Answer:  (a) ay + bx = ab

73. The graph of the equation x = 3 is:​

(a) a point

(b) straight line parallel to y axis

(c) straight line passing through the origin

(d) straight line parallel to x axis

Answer: (b) straight line parallel to y axis

74. The horizontal and vertical lines drawn to determine the position of a point in a Cartesian plane are called​

(a) Intersecting lines

(b) Transversals

(c) Perpendicular lines

(d) X-axis and Y-axis

75. he line segment joining (2, – 3) and (5, 6) is divided by x-axis in the ratio:

(a) 2 : 1

(b) 3 : 1

(c) 1 : 2

(d) 1 : 3

76. If A and B are the points (-6, 7) and (-1, -5) respectively, then the distance 2AB is equal to​

(a) 26

(b) 169

(c) 13

(d) 238

77. Three consecutive vertices of a parallelogram are (1, –2), (3, 6) and (5, 10). The coordinates of the fourth vertex are :

(a) (–3, 2)

(b) (2, – 3)

(c) (3, 2)

(d) (–2, –3)

78. The distance between the points (3,4) and (8,-6) is​

(a) 2√5 units

(b) 3√5 units

(c) √5 units

(d) 5√5 units

79.  The perimeter of the triangle formed by the points A(0,0), B(1,0) and C(0,1) is

(a) √2 + 1

(b) 1 ± √2

(c) 2 + √2

(d) 3

80. The values of x and y, if the distance of the point (x,y) from (-3,0) as well as from (3,0) is 4 are

(a) x = 1, y = 7

(b) x = 2, y = 7

(c) x = 0, y = – √7

(d) x = 0, y = ± √7

Answer: (d) x = 0, y = ± √7