Coordinate Geometry Worksheet for Maths Olympiad

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

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