Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 334 · 40 questions

How to solve it (Across, up, Pythagoras): Distance: across = difference of the x values, up = difference of the y values; distance = √(across² + up²). Midpoint = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). Quadrants by signs: (+, +) first, (−, +) second, (−, −) third, (+, −) fourth.

1. 1.What is the midpoint of the line joining (7, 1) and (15, 13)? (a) (4, 6) (b) (11, 7) (c) (22, 14) (d) (7, 11)
2. 2.In which quadrant does the point (−7, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
3. 3.What is the distance between the points (8, 18) and (20, 9)? (a) 21 (b) 225 (c) 16 (d) 15
4. 4.What is the distance between the points (2, 4) and (8, 12)? (a) 10 (b) 14 (c) 100 (d) 11
5. 5.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
6. 6.What is the distance between the points (2, 4) and (17, 12)? (a) 23 (b) 289 (c) 18 (d) 17
7. 7.What is the distance between the points (2, 18) and (14, 9)? (a) 225 (b) 16 (c) 15 (d) 21
8. 8.What is the midpoint of the line joining (4, 7) and (6, 5)? (a) (5, 6) (b) (1, 1) (c) (10, 12) (d) (6, 5)
9. 9.What is the distance between the points (9, 9) and (15, 1)? (a) 11 (b) 10 (c) 14 (d) 100
10. 10.What is the distance between the points (2, 16) and (14, 7)? (a) 15 (b) 21 (c) 16 (d) 225
11. 11.What is the distance between the points (1, 0) and (8, 24)? (a) 25 (b) 625 (c) 26 (d) 31
12. 12.What is the midpoint of the line joining (2, 0) and (14, 8)? (a) (16, 8) (b) (4, 8) (c) (6, 4) (d) (8, 4)
13. 13.In which quadrant does the point (−4, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
14. 14.What is the distance between the points (7, 7) and (11, 4)? (a) 25 (b) 6 (c) 5 (d) 7
15. 15.What is the midpoint of the line joining (8, 14) and (12, 4)? (a) (10, 9) (b) (2, 5) (c) (20, 18) (d) (9, 10)
16. 16.What is the midpoint of the line joining (2, 7) and (10, 9)? (a) (8, 6) (b) (4, 1) (c) (12, 16) (d) (6, 8)
17. 17.What is the midpoint of the line joining (3, 5) and (7, 1)? (a) (5, 3) (b) (10, 6) (c) (3, 5) (d) (2, 2)
18. 18.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
19. 19.What is the midpoint of the line joining (5, 9) and (17, 21)? (a) (11, 15) (b) (22, 30) (c) (6, 6) (d) (15, 11)
20. 20.In which quadrant does the point (−5, 4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
21. 21.In which quadrant does the point (4, −5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
22. 22.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
23. 23.What is the distance between the points (4, 8) and (9, 20)? (a) 169 (b) 13 (c) 17 (d) 14
24. 24.What is the distance between the points (5, 8) and (17, 13)? (a) 14 (b) 13 (c) 169 (d) 17
25. 25.What is the distance between the points (5, 12) and (14, 0)? (a) 21 (b) 225 (c) 15 (d) 16
26. 26.What is the distance between the points (8, 1) and (20, 10)? (a) 16 (b) 21 (c) 15 (d) 225
27. 27.In which quadrant does the point (3, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
28. 28.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
29. 29.What is the midpoint of the line joining (5, 9) and (15, 19)? (a) (14, 10) (b) (5, 5) (c) (20, 28) (d) (10, 14)
30. 30.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
31. 31.What is the distance between the points (5, 9) and (10, 21)? (a) 169 (b) 14 (c) 17 (d) 13
32. 32.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
33. 33.What is the midpoint of the line joining (0, 12) and (6, 8)? (a) (10, 3) (b) (3, 2) (c) (3, 10) (d) (6, 20)
34. 34.In which quadrant does the point (3, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
35. 35.In which quadrant does the point (5, −7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
36. 36.What is the midpoint of the line joining (0, 3) and (12, 5)? (a) (6, 1) (b) (4, 6) (c) (12, 8) (d) (6, 4)
37. 37.What is the distance between the points (2, 9) and (5, 5)? (a) 6 (b) 25 (c) 5 (d) 7
38. 38.What is the midpoint of the line joining (1, 4) and (13, 0)? (a) (2, 7) (b) (6, 2) (c) (7, 2) (d) (14, 4)
39. 39.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
40. 40.What is the midpoint of the line joining (8, 12) and (16, 2)? (a) (7, 12) (b) (24, 14) (c) (4, 5) (d) (12, 7)

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