Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 337 · 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 (10, 16) and (14, 8)? (a) (2, 4) (b) (24, 24) (c) (12, 12) (d) (13, 12)
2. 2.What is the distance between the points (1, 10) and (25, 3)? (a) 625 (b) 25 (c) 31 (d) 26
3. 3.In which quadrant does the point (−1, 8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
4. 4.What is the distance between the points (6, 3) and (14, 18)? (a) 17 (b) 289 (c) 18 (d) 23
5. 5.What is the midpoint of the line joining (5, 4) and (7, 10)? (a) (7, 6) (b) (1, 3) (c) (12, 14) (d) (6, 7)
6. 6.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
7. 7.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 21 (d) 225
8. 8.In which quadrant does the point (−7, 8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
9. 9.What is the distance between the points (1, 9) and (8, 33)? (a) 25 (b) 625 (c) 26 (d) 31
10. 10.What is the distance between the points (1, 5) and (13, 0)? (a) 169 (b) 17 (c) 14 (d) 13
11. 11.What is the midpoint of the line joining (0, 9) and (4, 5)? (a) (4, 14) (b) (2, 7) (c) (2, 2) (d) (7, 2)
12. 12.In which quadrant does the point (8, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
13. 13.What is the midpoint of the line joining (7, 22) and (11, 10)? (a) (16, 9) (b) (9, 16) (c) (18, 32) (d) (2, 6)
14. 14.In which quadrant does the point (6, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
15. 15.What is the distance between the points (5, 24) and (13, 9)? (a) 18 (b) 289 (c) 17 (d) 23
16. 16.What is the midpoint of the line joining (6, 14) and (8, 4)? (a) (1, 5) (b) (14, 18) (c) (9, 7) (d) (7, 9)
17. 17.What is the midpoint of the line joining (5, 0) and (13, 12)? (a) (6, 9) (b) (4, 6) (c) (9, 6) (d) (18, 12)
18. 18.What is the distance between the points (3, 9) and (15, 4)? (a) 169 (b) 13 (c) 14 (d) 17
19. 19.In which quadrant does the point (9, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
20. 20.What is the midpoint of the line joining (6, 2) and (12, 14)? (a) (18, 16) (b) (3, 6) (c) (9, 8) (d) (8, 9)
21. 21.In which quadrant does the point (2, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
22. 22.What is the distance between the points (3, 4) and (7, 7)? (a) 6 (b) 25 (c) 5 (d) 7
23. 23.What is the midpoint of the line joining (8, 7) and (20, 17)? (a) (6, 5) (b) (14, 12) (c) (12, 14) (d) (28, 24)
24. 24.In which quadrant does the point (−7, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
25. 25.What is the distance between the points (5, 2) and (10, 14)? (a) 17 (b) 13 (c) 169 (d) 14
26. 26.What is the distance between the points (1, 1) and (13, 10)? (a) 15 (b) 16 (c) 21 (d) 225
27. 27.What is the midpoint of the line joining (8, 3) and (20, 9)? (a) (6, 3) (b) (14, 6) (c) (6, 14) (d) (28, 12)
28. 28.What is the midpoint of the line joining (10, 0) and (18, 12)? (a) (14, 6) (b) (6, 14) (c) (4, 6) (d) (28, 12)
29. 29.In which quadrant does the point (−9, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
30. 30.What is the distance between the points (2, 3) and (7, 15)? (a) 169 (b) 13 (c) 14 (d) 17
31. 31.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
32. 32.In which quadrant does the point (8, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
33. 33.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
34. 34.What is the midpoint of the line joining (4, 11) and (16, 5)? (a) (8, 10) (b) (6, 3) (c) (20, 16) (d) (10, 8)
35. 35.In which quadrant does the point (−3, 6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
36. 36.What is the midpoint of the line joining (5, 17) and (17, 7)? (a) (12, 11) (b) (22, 24) (c) (11, 12) (d) (6, 5)
37. 37.What is the distance between the points (0, 21) and (5, 9)? (a) 169 (b) 17 (c) 13 (d) 14
38. 38.What is the midpoint of the line joining (5, 10) and (11, 14)? (a) (8, 12) (b) (3, 2) (c) (16, 24) (d) (12, 8)
39. 39.What is the distance between the points (2, 5) and (6, 8)? (a) 7 (b) 25 (c) 5 (d) 6
40. 40.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100

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