Coordinate Geometry MCQs Mock Test of 10th Class Mathematics

Welcome to your Coordinate Geometry MCQs Mock Test of 10th Class Mathematics

1.

1. The area of a triangle with vertices (a, b + c), (b, c + a) and (c, a + b) is

(A) (a + b + c)2

(B) 0

(C) a + b + c

(D) ab

2.

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

(a) 2

(b) 3

(c) 1

(d) 5

3.

3. The point which lies on the perpendicular bisector of the line segment joining the points A(–2, –5) and B(2, 5) is

(a) (0, 0)

(b) (0, 2)

(c) (2, 0)

(d) (–2, 0)

4.

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

(a) 4

(b) 5

(c) 6

(d) 3√3

5.

5. If the points A(1, 2), O(0, 0) and C(a, b) are collinear, then

(a) a = b

(b) a = 2b

(c) 2a = b

(d) a = –b

6.

6. 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

7.

7. 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

8.

8. 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

9.

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

(a) α + β

(b) α² + β²

(c) |α| + |β|

(d) α2+β2−−−−−−√

10.

10. 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

11.

11. 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)

12.

12. 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

13.

13. 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

14.

14. 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

15.

15. A line intersects the y-axis and x-axis at the points P and Q, respectively. If (2, -5) is the midpoint 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)

16.

16. 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

17.

17. 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)

18.

18. 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)

19.

19. The perpendicular bisector of the line segment joining the points A(1, 5) and B(4, 6) cuts the y-axis at

(a) (0, 13)

(b) (0, –13)

(c) (0, 12)

(d) (13, 0)

20.

20. 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

21.

21. 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

22.

22. 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)

23.

23. 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

24.

24. 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)

25.

25. 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

26.

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

(A) 2

(B) 3

(C) 1

(D) 5

27.

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

(A) 6

(B) 8

(C) 4

(D) 2

28.

28. AOBC is a rectangle whose three vertices are vertices 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.

29. 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

30.

30. The coordinates of the point which is equidistant from the three vertices of the Δ AOB as shown in the figure is:

(A) (x, y)

(B) (y, x)

(C) (x/2, y/2)

(D) (y/2, x/2)

31.

31. 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

32.

32. 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

33.

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

(A) I quadrant

(B) II quadrant

(C) III quadrant

(D) IV quadrant

34.

34. 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)

35.

35. 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)

36.

36. The ratio in which the point P (3/4, 5/12)divides the line segment joining the Points A (1/2, 3/2) and B (2, –5) is:

(A) 1:5

(B) 5:1

(C) 1:3

(D) 3:1

37.

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

(a) Square

(b) Rectangle

(c) Parallelogram

(d) Rhombus

38.

38. If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then the value of x is:

(a) 2

(b) -2

(c) 1

(d) -1

39.

39. 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)

40.

40. The distance of point A(2, 4) from x-axis is

(a) 2 units

(b) 4 units

(c) -2 units

(d) -4 units

41.

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

(a) 4√10

(b) 2√10

(c) √10

(d) 20

42.

42. 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

43.

43. 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)

44.

44.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

45.

45. 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)

46.

46. 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

47.

47. The distance of the point P(–6, 8) from the origin is

(a) 8 units

(b) 2√7 units

(c) 10 units

(d) 6 units

48.

48. The distance between the points (0, 5) and (–5, 0) is

(a) 5 units

(b) 5√2 units

(c) 2√5 units

(d) 10 units

49.

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

(a) 5

(b) 12

(c) 11

(d) 7 + √5

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