Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 53 · 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 distance between the points (8, 21) and (16, 6)? (a) 18 (b) 17 (c) 289 (d) 23
2. 2.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
3. 3.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
4. 4.In which quadrant does the point (9, 8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
5. 5.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
6. 6.In which quadrant does the point (5, −3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
7. 7.In which quadrant does the point (−7, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
8. 8.What is the midpoint of the line joining (1, 2) and (5, 4)? (a) (4, 3) (b) (2, 1) (c) (3, 3) (d) (6, 6)
9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
10. 10.What is the midpoint of the line joining (2, 9) and (10, 19)? (a) (4, 5) (b) (12, 28) (c) (6, 14) (d) (14, 6)
11. 11.What is the midpoint of the line joining (9, 8) and (17, 12)? (a) (26, 20) (b) (10, 13) (c) (13, 10) (d) (4, 2)
12. 12.What is the distance between the points (5, 8) and (21, 20)? (a) 21 (b) 400 (c) 20 (d) 28
13. 13.In which quadrant does the point (4, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
14. 14.What is the distance between the points (7, 1) and (13, 9)? (a) 100 (b) 10 (c) 11 (d) 14
15. 15.What is the midpoint of the line joining (7, 3) and (13, 1)? (a) (10, 2) (b) (2, 10) (c) (3, 1) (d) (20, 4)
16. 16.In which quadrant does the point (7, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
17. 17.What is the distance between the points (6, 5) and (18, 14)? (a) 16 (b) 15 (c) 21 (d) 225
18. 18.In which quadrant does the point (−4, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
19. 19.In which quadrant does the point (−4, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
20. 20.What is the distance between the points (9, 3) and (21, 8)? (a) 169 (b) 13 (c) 17 (d) 14
21. 21.What is the midpoint of the line joining (8, 7) and (10, 17)? (a) (12, 9) (b) (18, 24) (c) (1, 5) (d) (9, 12)
22. 22.In which quadrant does the point (2, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
23. 23.What is the midpoint of the line joining (7, 6) and (17, 18)? (a) (13, 12) (b) (5, 6) (c) (12, 12) (d) (24, 24)
24. 24.What is the midpoint of the line joining (6, 5) and (14, 3)? (a) (4, 10) (b) (4, 1) (c) (20, 8) (d) (10, 4)
25. 25.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
26. 26.In which quadrant does the point (7, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
27. 27.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
28. 28.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
29. 29.What is the midpoint of the line joining (6, 14) and (10, 10)? (a) (16, 24) (b) (8, 12) (c) (2, 2) (d) (12, 8)
30. 30.What is the distance between the points (4, 3) and (19, 11)? (a) 23 (b) 289 (c) 18 (d) 17
31. 31.What is the distance between the points (4, 9) and (12, 3)? (a) 14 (b) 11 (c) 100 (d) 10
32. 32.What is the distance between the points (3, 16) and (19, 4)? (a) 400 (b) 28 (c) 21 (d) 20
33. 33.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
34. 34.What is the distance between the points (8, 11) and (20, 2)? (a) 21 (b) 16 (c) 225 (d) 15
35. 35.In which quadrant does the point (2, 5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
36. 36.What is the midpoint of the line joining (2, 9) and (4, 11)? (a) (3, 10) (b) (1, 1) (c) (6, 20) (d) (10, 3)
37. 37.In which quadrant does the point (5, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
38. 38.In which quadrant does the point (−2, 6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
39. 39.What is the midpoint of the line joining (1, 6) and (11, 12)? (a) (5, 3) (b) (12, 18) (c) (9, 6) (d) (6, 9)
40. 40.In which quadrant does the point (−9, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant

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