Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 420 · 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 (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
2. 2.What is the midpoint of the line joining (2, 9) and (14, 15)? (a) (8, 12) (b) (6, 3) (c) (12, 8) (d) (16, 24)
3. 3.What is the distance between the points (2, 6) and (5, 2)? (a) 6 (b) 25 (c) 7 (d) 5
4. 4.What is the distance between the points (2, 9) and (14, 0)? (a) 21 (b) 225 (c) 16 (d) 15
5. 5.What is the midpoint of the line joining (10, 15) and (12, 7)? (a) (12, 11) (b) (22, 22) (c) (1, 4) (d) (11, 11)
6. 6.In which quadrant does the point (5, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
7. 7.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
8. 8.What is the distance between the points (1, 22) and (13, 6)? (a) 400 (b) 20 (c) 28 (d) 21
9. 9.In which quadrant does the point (4, 6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
10. 10.In which quadrant does the point (8, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
11. 11.In which quadrant does the point (6, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
12. 12.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
13. 13.What is the distance between the points (0, 4) and (6, 12)? (a) 100 (b) 14 (c) 10 (d) 11
14. 14.What is the distance between the points (5, 7) and (14, 19)? (a) 225 (b) 16 (c) 21 (d) 15
15. 15.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
16. 16.What is the midpoint of the line joining (0, 6) and (4, 2)? (a) (4, 8) (b) (2, 4) (c) (4, 2) (d) (2, 2)
17. 17.What is the midpoint of the line joining (6, 10) and (12, 12)? (a) (18, 22) (b) (9, 11) (c) (3, 1) (d) (11, 9)
18. 18.In which quadrant does the point (−2, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
19. 19.What is the midpoint of the line joining (3, 3) and (15, 11)? (a) (9, 7) (b) (18, 14) (c) (7, 9) (d) (6, 4)
20. 20.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
21. 21.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
22. 22.In which quadrant does the point (−3, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
23. 23.What is the distance between the points (7, 13) and (12, 1)? (a) 14 (b) 17 (c) 13 (d) 169
24. 24.What is the distance between the points (4, 17) and (12, 2)? (a) 18 (b) 289 (c) 23 (d) 17
25. 25.In which quadrant does the point (4, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
26. 26.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
27. 27.What is the midpoint of the line joining (3, 9) and (7, 15)? (a) (2, 3) (b) (5, 12) (c) (10, 24) (d) (12, 5)
28. 28.In which quadrant does the point (−1, −6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
29. 29.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
30. 30.In which quadrant does the point (9, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
31. 31.In which quadrant does the point (3, 5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
32. 32.What is the midpoint of the line joining (0, 11) and (2, 9)? (a) (1, 10) (b) (2, 20) (c) (10, 1) (d) (1, 1)
33. 33.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
34. 34.What is the midpoint of the line joining (3, 0) and (7, 12)? (a) (6, 5) (b) (2, 6) (c) (10, 12) (d) (5, 6)
35. 35.In which quadrant does the point (9, −9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
36. 36.What is the distance between the points (4, 9) and (9, 21)? (a) 13 (b) 17 (c) 169 (d) 14
37. 37.What is the midpoint of the line joining (10, 4) and (16, 16)? (a) (10, 13) (b) (13, 10) (c) (26, 20) (d) (3, 6)
38. 38.In which quadrant does the point (−9, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
39. 39.What is the distance between the points (2, 9) and (14, 14)? (a) 13 (b) 169 (c) 17 (d) 14
40. 40.What is the distance between the points (3, 1) and (18, 9)? (a) 18 (b) 289 (c) 17 (d) 23

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