Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 498 · 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 (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
3. 3.What is the distance between the points (6, 9) and (10, 6)? (a) 5 (b) 7 (c) 6 (d) 25
4. 4.What is the distance between the points (9, 24) and (17, 9)? (a) 18 (b) 289 (c) 23 (d) 17
5. 5.What is the distance between the points (9, 7) and (21, 2)? (a) 14 (b) 169 (c) 13 (d) 17
6. 6.What is the midpoint of the line joining (10, 18) and (12, 10)? (a) (1, 4) (b) (14, 11) (c) (11, 14) (d) (22, 28)
7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
8. 8.In which quadrant does the point (7, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
9. 9.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
10. 10.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
11. 11.What is the distance between the points (4, 16) and (10, 8)? (a) 14 (b) 11 (c) 100 (d) 10
12. 12.What is the distance between the points (6, 7) and (18, 16)? (a) 21 (b) 15 (c) 16 (d) 225
13. 13.What is the midpoint of the line joining (2, 0) and (12, 6)? (a) (3, 7) (b) (5, 3) (c) (14, 6) (d) (7, 3)
14. 14.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
15. 15.In which quadrant does the point (1, 2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
16. 16.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
17. 17.In which quadrant does the point (−4, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
18. 18.In which quadrant does the point (−8, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
19. 19.What is the distance between the points (6, 10) and (14, 4)? (a) 10 (b) 11 (c) 100 (d) 14
20. 20.What is the distance between the points (8, 4) and (15, 28)? (a) 26 (b) 625 (c) 31 (d) 25
21. 21.What is the midpoint of the line joining (1, 10) and (9, 0)? (a) (5, 5) (b) (6, 5) (c) (10, 10) (d) (4, 5)
22. 22.What is the distance between the points (6, 4) and (13, 28)? (a) 625 (b) 25 (c) 26 (d) 31
23. 23.What is the distance between the points (3, 6) and (11, 21)? (a) 17 (b) 18 (c) 289 (d) 23
24. 24.What is the distance between the points (0, 8) and (3, 4)? (a) 25 (b) 6 (c) 7 (d) 5
25. 25.What is the midpoint of the line joining (7, 5) and (9, 1)? (a) (1, 2) (b) (8, 3) (c) (3, 8) (d) (16, 6)
26. 26.What is the distance between the points (3, 10) and (27, 3)? (a) 625 (b) 25 (c) 26 (d) 31
27. 27.In which quadrant does the point (−7, 5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
28. 28.In which quadrant does the point (−3, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
29. 29.In which quadrant does the point (8, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
30. 30.What is the distance between the points (8, 18) and (13, 6)? (a) 14 (b) 169 (c) 17 (d) 13
31. 31.In which quadrant does the point (6, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
32. 32.What is the distance between the points (2, 7) and (26, 14)? (a) 31 (b) 25 (c) 26 (d) 625
33. 33.What is the midpoint of the line joining (6, 6) and (18, 10)? (a) (24, 16) (b) (12, 8) (c) (8, 12) (d) (6, 2)
34. 34.What is the distance between the points (8, 16) and (20, 7)? (a) 21 (b) 16 (c) 225 (d) 15
35. 35.What is the distance between the points (4, 9) and (28, 16)? (a) 26 (b) 31 (c) 625 (d) 25
36. 36.What is the midpoint of the line joining (5, 4) and (17, 2)? (a) (11, 3) (b) (3, 11) (c) (6, 1) (d) (22, 6)
37. 37.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
38. 38.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
39. 39.What is the distance between the points (6, 2) and (9, 6)? (a) 7 (b) 5 (c) 6 (d) 25
40. 40.What is the midpoint of the line joining (7, 10) and (15, 18)? (a) (14, 11) (b) (4, 4) (c) (11, 14) (d) (22, 28)

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