MATHEMATICS CLASS- 10
MCQ- CH-7(Coordinate-Geometry)
Class 10 Mathematics
Chapter 7: Coordinate Geometry
50 Board-Level MCQs with Answers and Solutions
Q1. The distance between the points (0, 0) and (3, 4) is
(a) 4
(b) 5
(c) 6
(d) 7
Answer: (b) 5
Solution: Distance = √[(3−0)² + (4−0)²] = √25 = 5.
Q2. The coordinates of the midpoint of (2, 4) and (6, 8) are
(a) (4, 6)
(b) (3, 5)
(c) (5, 7)
(d) (4, 5)
Answer: (a) (4, 6)
Q3. Distance between (1, 2) and (1, 8) is
(a) 5
(b) 6
(c) 7
(d) 8
Answer: (b) 6
Q4. The midpoint of the line joining (-2, 5) and (4, 7) is
(a) (1, 6)
(b) (2, 6)
(c) (1, 5)
(d) (2, 5)
Answer: (a) (1, 6)
Q5. Distance between (0, 0) and (5, 12) is
(a) 12
(b) 13
(c) 14
(d) 15
Answer: (b) 13
Q6. The point dividing the segment joining A and B into two equal parts is called
(a) Origin
(b) Midpoint
(c) Centroid
(d) Focus
Answer: (b) Midpoint
Q7. The midpoint of (4, 2) and (8, 10) is
(a) (5, 6)
(b) (6, 6)
(c) (6, 7)
(d) (7, 6)
Answer: (b) (6, 6)
Q8. Distance between (-3, 4) and (3, 4) is
(a) 3
(b) 4
(c) 5
(d) 6
Answer: (d) 6
Q9. The midpoint of (0, 0) and (10, 10) is
(a) (5, 5)
(b) (10, 10)
(c) (0, 0)
(d) (4, 4)
Answer: (a) (5, 5)
Q10. Distance between (2, 3) and (5, 7) is
(a) 4
(b) 5
(c) 6
(d) 7
Answer: (b) 5
Q11. The coordinates of the origin are
(a) (1, 0)
(b) (0, 1)
(c) (0, 0)
(d) (1, 1)
Answer: (c) (0, 0)
Q12. Distance between (4, 0) and (0, 3) is
(a) 4
(b) 5
(c) 6
(d) 7
Answer: (b) 5
Q13. The midpoint of (-6, 2) and (4, 8) is
(a) (-1, 5)
(b) (0, 5)
(c) (1, 4)
(d) (-1, 4)
Answer: (a) (-1, 5)
Q14. Distance between (7, 2) and (7, 10) is
(a) 6
(b) 7
(c) 8
(d) 9
Answer: (c) 8
Q15. If the midpoint of A(2, y) and B(6, 8) is (4, 6), then y equals
(a) 2
(b) 4
(c) 6
(d) 8
Answer: (b) 4
Q16. Distance between (-1, -1) and (2, 3) is
(a) 4
(b) 5
(c) 6
(d) 7
Answer: (b) 5
Q17. Which formula is used to find distance between two points?
(a) √(x²+y²)
(b) √[(x₂−x₁)²+(y₂−y₁)²]
(c) (x+y)/2
(d) x²+y²
Answer: (b)
Q18. Midpoint of (3, 5) and (7, 9) is
(a) (4, 7)
(b) (5, 7)
(c) (6, 7)
(d) (5, 8)
Answer: (b) (5, 7)
Q19. Distance between (0, 5) and (12, 5) is
(a) 10
(b) 11
(c) 12
(d) 13
Answer: (c) 12
Q20. If A(1, 2), B(4, 6), then AB equals
(a) 3
(b) 4
(c) 5
(d) 6
Answer: (c) 5
Q21. (CBSE PYQ) The midpoint of (-4, -2) and (6, 8) is
(a) (1, 3)
(b) (2, 3)
(c) (1, 4)
(d) (2, 4)
Answer: (a) (1, 3)
Q22. Distance between (-3, -4) and (0, 0) is
(a) 3
(b) 4
(c) 5
(d) 6
Answer: (c) 5
Q23. The midpoint formula is
(a) ((x₁+x₂)/2 , (y₁+y₂)/2)
(b) ((x₁−x₂)/2 , (y₁−y₂)/2)
(c) (x₁+x₂, y₁+y₂)
(d) (x₁−x₂, y₁−y₂)
Answer: (a)
Q24. If midpoint of A(2, 4) and B(x, 8) is (5, 6), then x equals
(a) 6
(b) 7
(c) 8
(d) 9
Answer: (c) 8
Q25. Distance between (5, 5) and (8, 9) is
(a) 3
(b) 4
(c) 5
(d) 6
Answer: (c) 5
Q26. (CBSE PYQ) If P(2, 3) and Q(8, 11), then PQ is
(a) 8
(b) 9
(c) 10
(d) 12
Answer: (c) 10
Q27. Midpoint of (-2, -6) and (4, 2) is
(a) (1, -2)
(b) (2, -1)
(c) (1, -1)
(d) (0, -2)
Answer: (a)
Q28. Distance between (1,1) and (4,5) is
(a) 4
(b) 5
(c) 6
(d) 7
Answer: (b)
Q29. The midpoint of (a,b) and (c,d) is
(a) ((a+c)/2,(b+d)/2)
(b) ((a−c)/2,(b−d)/2)
(c) (a+c,b+d)
(d) (a−c,b−d)
Answer: (a)
Q30. Distance between (6, 8) and (0, 0) is
(a) 8
(b) 9
(c) 10
(d) 12
Answer: (c)
Q31. A point on x-axis has
(a) x = 0
(b) y = 0
(c) x = y
(d) x = 1
Answer: (b)
Q32. A point on y-axis has
(a) x = 0
(b) y = 0
(c) x = y
(d) y = 1
Answer: (a)
Q33. Distance between (-5, 0) and (5, 0) is
(a) 5
(b) 8
(c) 10
(d) 12
Answer: (c)
Q34. Midpoint of (-8, 4) and (2, 10) is
(a) (-3, 7)
(b) (-2, 7)
(c) (-3, 8)
(d) (-2, 8)
Answer: (a)
Q35. Distance between (3, -4) and (0, 0) is
(a) 3
(b) 4
(c) 5
(d) 6
Answer: (c)
Q36. (CBSE PYQ) The midpoint of (6, -2) and (-2, 6) is
(a) (2, 2)
(b) (1, 2)
(c) (2, 1)
(d) (0, 2)
Answer: (a)
Q37. If midpoint of (x, 2) and (6, 8) is (4, 5), then x equals
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (b)
Q38. Distance between (-2, 3) and (4, -5) is
(a) 8
(b) 10
(c) 12
(d) 14
Answer: (b)
Q39. The distance formula is derived using
(a) Midpoint Theorem
(b) Pythagoras Theorem
(c) BPT
(d) Similarity
Answer: (b)
Q40. Distance between (2, -1) and (5, 3) is
(a) 4
(b) 5
(c) 6
(d) 7
Answer: (b)
Q41. The midpoint of (10, 2) and (2, 10) is
(a) (6, 6)
(b) (5, 5)
(c) (4, 6)
(d) (6, 4)
Answer: (a)
Q42. (CBSE PYQ) Distance between (7, 24) and (0, 0) is
(a) 24
(b) 25
(c) 26
(d) 27
Answer: (b)
Q43. The coordinates of the midpoint of any diameter of a circle are the coordinates of its
(a) Radius
(b) Tangent
(c) Centre
(d) Chord
Answer: (c)
Q44. Distance between (1, 1) and (-2, -3) is
(a) 4
(b) 5
(c) 6
(d) 7
Answer: (b)
Q45. If A(0,0) and B(8,6), then midpoint is
(a) (4,3)
(b) (3,4)
(c) (4,4)
(d) (5,3)
Answer: (a)
Q46. Distance between (9,12) and origin is
(a) 12
(b) 13
(c) 15
(d) 18
Answer: (c)
Q47. The midpoint of (-4, 8) and (6, -2) is
(a) (1,3)
(b) (2,3)
(c) (1,2)
(d) (2,2)
Answer: (a)
Q48. If AB = 10 and midpoint M divides AB equally, then AM equals
(a) 2
(b) 4
(c) 5
(d) 10
Answer: (c)
Q49. Distance between (0, -5) and (12, 0) is
(a) 12
(b) 13
(c) 14
(d) 15
Answer: (b)
Q50. Which statement is true?
(a) Midpoint always lies outside the segment.
(b) Distance between a point and itself is 1.
(c) Distance can never be negative.
(d) Midpoint formula uses subtraction only.
Answer: (c) Distance can never be negative.
Solution: Distance represents length and is always non-negative.