Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 643 · 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 (0, 1) and (12, 5)? (a) (6, 3) (b) (6, 2) (c) (12, 6) (d) (3, 6)
2. 2.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
3. 3.In which quadrant does the point (−7, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
4. 4.In which quadrant does the point (6, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
5. 5.What is the distance between the points (3, 2) and (15, 7)? (a) 14 (b) 169 (c) 13 (d) 17
6. 6.In which quadrant does the point (−1, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
7. 7.What is the distance between the points (8, 14) and (23, 6)? (a) 23 (b) 18 (c) 17 (d) 289
8. 8.In which quadrant does the point (2, −1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
9. 9.What is the midpoint of the line joining (7, 4) and (9, 10)? (a) (8, 7) (b) (1, 3) (c) (7, 8) (d) (16, 14)
10. 10.In which quadrant does the point (8, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
11. 11.In which quadrant does the point (−5, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
12. 12.What is the distance between the points (3, 8) and (10, 32)? (a) 31 (b) 26 (c) 25 (d) 625
13. 13.What is the midpoint of the line joining (0, 19) and (6, 7)? (a) (3, 13) (b) (13, 3) (c) (3, 6) (d) (6, 26)
14. 14.What is the midpoint of the line joining (2, 8) and (12, 6)? (a) (5, 1) (b) (7, 7) (c) (8, 7) (d) (14, 14)
15. 15.In which quadrant does the point (−6, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
16. 16.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
17. 17.What is the distance between the points (9, 6) and (13, 9)? (a) 5 (b) 6 (c) 25 (d) 7
18. 18.What is the midpoint of the line joining (8, 14) and (12, 10)? (a) (2, 2) (b) (10, 12) (c) (12, 10) (d) (20, 24)
19. 19.In which quadrant does the point (2, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
20. 20.What is the distance between the points (0, 7) and (24, 0)? (a) 25 (b) 26 (c) 625 (d) 31
21. 21.What is the distance between the points (5, 8) and (13, 14)? (a) 14 (b) 10 (c) 11 (d) 100
22. 22.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
23. 23.In which quadrant does the point (6, −6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
24. 24.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
25. 25.What is the distance between the points (3, 15) and (18, 7)? (a) 17 (b) 23 (c) 18 (d) 289
26. 26.What is the distance between the points (7, 8) and (19, 17)? (a) 16 (b) 21 (c) 15 (d) 225
27. 27.What is the distance between the points (3, 8) and (7, 5)? (a) 25 (b) 6 (c) 5 (d) 7
28. 28.What is the midpoint of the line joining (7, 21) and (17, 9)? (a) (24, 30) (b) (5, 6) (c) (12, 15) (d) (15, 12)
29. 29.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
30. 30.What is the midpoint of the line joining (1, 4) and (3, 16)? (a) (1, 6) (b) (4, 20) (c) (10, 2) (d) (2, 10)
31. 31.What is the distance between the points (8, 3) and (32, 10)? (a) 625 (b) 25 (c) 26 (d) 31
32. 32.In which quadrant does the point (7, −9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
33. 33.In which quadrant does the point (6, 6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
34. 34.What is the midpoint of the line joining (4, 7) and (6, 11)? (a) (10, 18) (b) (1, 2) (c) (9, 5) (d) (5, 9)
35. 35.What is the midpoint of the line joining (8, 6) and (10, 10)? (a) (1, 2) (b) (18, 16) (c) (8, 9) (d) (9, 8)
36. 36.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
37. 37.What is the distance between the points (7, 6) and (12, 18)? (a) 169 (b) 17 (c) 14 (d) 13
38. 38.What is the midpoint of the line joining (8, 2) and (10, 4)? (a) (9, 3) (b) (18, 6) (c) (3, 9) (d) (1, 1)
39. 39.What is the midpoint of the line joining (6, 3) and (10, 7)? (a) (5, 8) (b) (8, 5) (c) (2, 2) (d) (16, 10)
40. 40.What is the midpoint of the line joining (0, 10) and (10, 8)? (a) (10, 18) (b) (5, 1) (c) (5, 9) (d) (9, 5)

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