Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 995 · 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, 16) and (8, 8)? (a) (12, 4) (b) (4, 4) (c) (4, 12) (d) (8, 24)
2. 2.What is the distance between the points (6, 2) and (11, 14)? (a) 169 (b) 17 (c) 14 (d) 13
3. 3.What is the midpoint of the line joining (10, 3) and (12, 7)? (a) (5, 11) (b) (1, 2) (c) (11, 5) (d) (22, 10)
4. 4.What is the midpoint of the line joining (1, 14) and (7, 10)? (a) (3, 2) (b) (12, 4) (c) (4, 12) (d) (8, 24)
5. 5.What is the midpoint of the line joining (2, 15) and (10, 9)? (a) (4, 3) (b) (12, 24) (c) (12, 6) (d) (6, 12)
6. 6.What is the midpoint of the line joining (1, 10) and (9, 12)? (a) (10, 22) (b) (5, 11) (c) (4, 1) (d) (11, 5)
7. 7.In which quadrant does the point (8, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
8. 8.In which quadrant does the point (8, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
9. 9.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
10. 10.What is the distance between the points (3, 6) and (19, 18)? (a) 20 (b) 21 (c) 28 (d) 400
11. 11.What is the midpoint of the line joining (4, 9) and (8, 19)? (a) (2, 5) (b) (12, 28) (c) (6, 14) (d) (14, 6)
12. 12.What is the distance between the points (4, 8) and (9, 20)? (a) 17 (b) 14 (c) 169 (d) 13
13. 13.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
14. 14.What is the midpoint of the line joining (7, 9) and (13, 21)? (a) (10, 15) (b) (3, 6) (c) (20, 30) (d) (15, 10)
15. 15.In which quadrant does the point (5, 7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
16. 16.In which quadrant does the point (5, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
17. 17.What is the midpoint of the line joining (1, 9) and (9, 13)? (a) (11, 5) (b) (4, 2) (c) (10, 22) (d) (5, 11)
18. 18.In which quadrant does the point (2, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
19. 19.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
20. 20.What is the midpoint of the line joining (6, 8) and (8, 16)? (a) (12, 7) (b) (7, 12) (c) (14, 24) (d) (1, 4)
21. 21.What is the distance between the points (0, 8) and (3, 4)? (a) 6 (b) 25 (c) 7 (d) 5
22. 22.What is the distance between the points (3, 3) and (8, 15)? (a) 169 (b) 17 (c) 13 (d) 14
23. 23.In which quadrant does the point (−6, 7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
24. 24.What is the distance between the points (5, 11) and (9, 8)? (a) 7 (b) 5 (c) 6 (d) 25
25. 25.What is the distance between the points (0, 15) and (8, 9)? (a) 100 (b) 14 (c) 10 (d) 11
26. 26.What is the distance between the points (6, 10) and (10, 7)? (a) 5 (b) 7 (c) 25 (d) 6
27. 27.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
28. 28.What is the distance between the points (9, 20) and (25, 8)? (a) 28 (b) 21 (c) 20 (d) 400
29. 29.What is the midpoint of the line joining (2, 2) and (6, 0)? (a) (1, 4) (b) (8, 2) (c) (2, 1) (d) (4, 1)
30. 30.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
31. 31.What is the distance between the points (7, 11) and (10, 7)? (a) 7 (b) 6 (c) 25 (d) 5
32. 32.What is the distance between the points (3, 11) and (7, 8)? (a) 7 (b) 5 (c) 6 (d) 25
33. 33.What is the distance between the points (1, 15) and (6, 3)? (a) 17 (b) 14 (c) 169 (d) 13
34. 34.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
35. 35.What is the midpoint of the line joining (3, 6) and (15, 2)? (a) (4, 9) (b) (9, 4) (c) (18, 8) (d) (6, 2)
36. 36.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
37. 37.In which quadrant does the point (3, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
38. 38.What is the distance between the points (0, 0) and (12, 9)? (a) 15 (b) 16 (c) 21 (d) 225
39. 39.What is the distance between the points (6, 8) and (18, 17)? (a) 21 (b) 15 (c) 16 (d) 225
40. 40.What is the distance between the points (5, 4) and (11, 12)? (a) 100 (b) 14 (c) 10 (d) 11

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