Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 449 · 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 midpoint of the line joining (2, 1) and (8, 5)? (a) (10, 6) (b) (3, 5) (c) (5, 3) (d) (3, 2)
2. 2.What is the distance between the points (4, 4) and (19, 12)? (a) 18 (b) 23 (c) 17 (d) 289
3. 3.What is the midpoint of the line joining (2, 0) and (10, 8)? (a) (4, 6) (b) (12, 8) (c) (4, 4) (d) (6, 4)
4. 4.In which quadrant does the point (7, 6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
5. 5.What is the distance between the points (7, 12) and (19, 7)? (a) 17 (b) 169 (c) 14 (d) 13
6. 6.In which quadrant does the point (6, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
7. 7.What is the midpoint of the line joining (10, 6) and (20, 10)? (a) (30, 16) (b) (5, 2) (c) (15, 8) (d) (8, 15)
8. 8.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
9. 9.What is the midpoint of the line joining (9, 0) and (15, 2)? (a) (3, 1) (b) (12, 1) (c) (24, 2) (d) (1, 12)
10. 10.In which quadrant does the point (1, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
11. 11.What is the midpoint of the line joining (3, 3) and (9, 7)? (a) (12, 10) (b) (3, 2) (c) (5, 6) (d) (6, 5)
12. 12.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
13. 13.In which quadrant does the point (4, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
14. 14.In which quadrant does the point (3, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
15. 15.What is the distance between the points (5, 2) and (20, 10)? (a) 289 (b) 18 (c) 23 (d) 17
16. 16.What is the distance between the points (2, 6) and (11, 18)? (a) 21 (b) 225 (c) 15 (d) 16
17. 17.What is the distance between the points (7, 10) and (22, 2)? (a) 289 (b) 17 (c) 18 (d) 23
18. 18.In which quadrant does the point (−7, −6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
19. 19.In which quadrant does the point (2, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
20. 20.What is the midpoint of the line joining (5, 2) and (13, 0)? (a) (1, 9) (b) (4, 1) (c) (9, 1) (d) (18, 2)
21. 21.What is the midpoint of the line joining (9, 5) and (21, 1)? (a) (6, 2) (b) (30, 6) (c) (3, 15) (d) (15, 3)
22. 22.What is the distance between the points (1, 10) and (5, 7)? (a) 5 (b) 7 (c) 25 (d) 6
23. 23.In which quadrant does the point (2, −6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
24. 24.In which quadrant does the point (−5, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
25. 25.In which quadrant does the point (−3, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
26. 26.In which quadrant does the point (−3, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
27. 27.What is the midpoint of the line joining (0, 10) and (2, 2)? (a) (6, 1) (b) (1, 4) (c) (2, 12) (d) (1, 6)
28. 28.What is the midpoint of the line joining (8, 0) and (18, 4)? (a) (26, 4) (b) (13, 2) (c) (2, 13) (d) (5, 2)
29. 29.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 14 (d) 17
30. 30.What is the distance between the points (8, 2) and (16, 8)? (a) 11 (b) 10 (c) 100 (d) 14
31. 31.What is the distance between the points (3, 16) and (12, 4)? (a) 225 (b) 21 (c) 15 (d) 16
32. 32.What is the midpoint of the line joining (3, 11) and (15, 7)? (a) (6, 2) (b) (18, 18) (c) (9, 9) (d) (10, 9)
33. 33.In which quadrant does the point (−4, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
34. 34.What is the distance between the points (7, 9) and (31, 16)? (a) 625 (b) 25 (c) 31 (d) 26
35. 35.In which quadrant does the point (−7, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
36. 36.What is the distance between the points (5, 5) and (17, 14)? (a) 21 (b) 15 (c) 16 (d) 225
37. 37.What is the distance between the points (2, 9) and (26, 16)? (a) 625 (b) 31 (c) 26 (d) 25
38. 38.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
39. 39.What is the midpoint of the line joining (6, 8) and (16, 10)? (a) (11, 9) (b) (22, 18) (c) (9, 11) (d) (5, 1)
40. 40.What is the distance between the points (3, 8) and (9, 16)? (a) 11 (b) 10 (c) 100 (d) 14

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