Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 934 · 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, 8) and (15, 32)? (a) 25 (b) 26 (c) 31 (d) 625
2. 2.What is the midpoint of the line joining (0, 7) and (12, 1)? (a) (6, 4) (b) (6, 3) (c) (12, 8) (d) (4, 6)
3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
4. 4.What is the distance between the points (2, 9) and (26, 2)? (a) 26 (b) 31 (c) 625 (d) 25
5. 5.What is the midpoint of the line joining (6, 18) and (14, 10)? (a) (4, 4) (b) (14, 10) (c) (10, 14) (d) (20, 28)
6. 6.What is the midpoint of the line joining (9, 9) and (11, 3)? (a) (20, 12) (b) (1, 3) (c) (6, 10) (d) (10, 6)
7. 7.What is the midpoint of the line joining (4, 14) and (14, 8)? (a) (11, 9) (b) (18, 22) (c) (9, 11) (d) (5, 3)
8. 8.In which quadrant does the point (8, −6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
9. 9.What is the midpoint of the line joining (10, 7) and (18, 9)? (a) (8, 14) (b) (28, 16) (c) (14, 8) (d) (4, 1)
10. 10.In which quadrant does the point (−8, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
11. 11.What is the distance between the points (2, 1) and (17, 9)? (a) 18 (b) 23 (c) 17 (d) 289
12. 12.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
13. 13.In which quadrant does the point (5, −6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
14. 14.In which quadrant does the point (2, 7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
15. 15.What is the midpoint of the line joining (7, 7) and (11, 5)? (a) (6, 9) (b) (2, 1) (c) (9, 6) (d) (18, 12)
16. 16.What is the distance between the points (7, 7) and (22, 15)? (a) 289 (b) 23 (c) 18 (d) 17
17. 17.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
18. 18.What is the midpoint of the line joining (4, 6) and (12, 18)? (a) (4, 6) (b) (12, 8) (c) (16, 24) (d) (8, 12)
19. 19.In which quadrant does the point (−8, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
20. 20.What is the midpoint of the line joining (9, 9) and (17, 17)? (a) (26, 26) (b) (4, 4) (c) (13, 13) (d) (14, 13)
21. 21.In which quadrant does the point (2, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
22. 22.What is the midpoint of the line joining (10, 7) and (20, 13)? (a) (30, 20) (b) (15, 10) (c) (10, 15) (d) (5, 3)
23. 23.What is the distance between the points (7, 14) and (15, 8)? (a) 11 (b) 14 (c) 100 (d) 10
24. 24.In which quadrant does the point (1, −4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
25. 25.What is the midpoint of the line joining (5, 7) and (7, 9)? (a) (8, 6) (b) (12, 16) (c) (6, 8) (d) (1, 1)
26. 26.What is the distance between the points (1, 30) and (8, 6)? (a) 31 (b) 26 (c) 25 (d) 625
27. 27.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
28. 28.What is the distance between the points (5, 15) and (21, 3)? (a) 21 (b) 400 (c) 28 (d) 20
29. 29.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
30. 30.What is the midpoint of the line joining (0, 3) and (10, 15)? (a) (5, 6) (b) (10, 18) (c) (9, 5) (d) (5, 9)
31. 31.What is the distance between the points (0, 0) and (8, 15)? (a) 18 (b) 23 (c) 289 (d) 17
32. 32.In which quadrant does the point (5, −9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
33. 33.What is the midpoint of the line joining (6, 6) and (12, 12)? (a) (10, 9) (b) (18, 18) (c) (9, 9) (d) (3, 3)
34. 34.What is the midpoint of the line joining (2, 5) and (14, 13)? (a) (9, 8) (b) (6, 4) (c) (16, 18) (d) (8, 9)
35. 35.In which quadrant does the point (−1, 8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
36. 36.What is the midpoint of the line joining (0, 19) and (6, 7)? (a) (6, 26) (b) (3, 6) (c) (13, 3) (d) (3, 13)
37. 37.In which quadrant does the point (3, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
38. 38.In which quadrant does the point (9, −5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
39. 39.What is the midpoint of the line joining (9, 14) and (17, 8)? (a) (4, 3) (b) (13, 11) (c) (26, 22) (d) (11, 13)
40. 40.What is the distance between the points (6, 26) and (13, 2)? (a) 25 (b) 31 (c) 26 (d) 625

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