Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 124 · 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.In which quadrant does the point (8, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
2. 2.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
3. 3.What is the midpoint of the line joining (4, 3) and (8, 11)? (a) (7, 6) (b) (12, 14) (c) (6, 7) (d) (2, 4)
4. 4.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
5. 5.What is the distance between the points (3, 16) and (15, 0)? (a) 28 (b) 400 (c) 20 (d) 21
6. 6.What is the distance between the points (2, 3) and (7, 15)? (a) 17 (b) 169 (c) 13 (d) 14
7. 7.What is the midpoint of the line joining (2, 12) and (12, 0)? (a) (7, 6) (b) (6, 7) (c) (14, 12) (d) (5, 6)
8. 8.What is the distance between the points (8, 7) and (11, 3)? (a) 6 (b) 5 (c) 25 (d) 7
9. 9.What is the midpoint of the line joining (4, 8) and (10, 6)? (a) (14, 14) (b) (8, 7) (c) (7, 7) (d) (3, 1)
10. 10.In which quadrant does the point (9, −9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
11. 11.What is the midpoint of the line joining (10, 8) and (12, 20)? (a) (11, 14) (b) (1, 6) (c) (22, 28) (d) (14, 11)
12. 12.In which quadrant does the point (−4, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
13. 13.In which quadrant does the point (2, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
14. 14.In which quadrant does the point (3, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
15. 15.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
16. 16.In which quadrant does the point (−9, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
17. 17.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 16 (d) 21
18. 18.In which quadrant does the point (−6, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
19. 19.In which quadrant does the point (6, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
20. 20.What is the midpoint of the line joining (7, 16) and (19, 8)? (a) (26, 24) (b) (6, 4) (c) (12, 13) (d) (13, 12)
21. 21.What is the midpoint of the line joining (8, 5) and (16, 15)? (a) (24, 20) (b) (12, 10) (c) (4, 5) (d) (10, 12)
22. 22.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
23. 23.What is the distance between the points (4, 8) and (19, 0)? (a) 289 (b) 17 (c) 18 (d) 23
24. 24.What is the midpoint of the line joining (0, 10) and (12, 18)? (a) (12, 28) (b) (6, 4) (c) (14, 6) (d) (6, 14)
25. 25.In which quadrant does the point (1, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
26. 26.What is the midpoint of the line joining (0, 18) and (2, 6)? (a) (1, 6) (b) (12, 1) (c) (1, 12) (d) (2, 24)
27. 27.What is the distance between the points (6, 18) and (11, 6)? (a) 169 (b) 17 (c) 13 (d) 14
28. 28.In which quadrant does the point (−7, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
29. 29.What is the midpoint of the line joining (1, 12) and (3, 8)? (a) (2, 10) (b) (4, 20) (c) (10, 2) (d) (1, 2)
30. 30.In which quadrant does the point (−3, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
31. 31.What is the distance between the points (2, 2) and (8, 10)? (a) 10 (b) 14 (c) 11 (d) 100
32. 32.What is the distance between the points (9, 3) and (25, 15)? (a) 28 (b) 400 (c) 20 (d) 21
33. 33.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
34. 34.What is the midpoint of the line joining (8, 8) and (20, 4)? (a) (6, 14) (b) (14, 6) (c) (6, 2) (d) (28, 12)
35. 35.In which quadrant does the point (8, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
36. 36.What is the distance between the points (8, 3) and (16, 18)? (a) 289 (b) 18 (c) 17 (d) 23
37. 37.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
38. 38.In which quadrant does the point (5, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
39. 39.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
40. 40.In which quadrant does the point (−2, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant

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