Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 370 · 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 (9, 9) and (12, 13)? (a) 25 (b) 5 (c) 6 (d) 7
2. 2.What is the distance between the points (9, 3) and (21, 12)? (a) 21 (b) 15 (c) 16 (d) 225
3. 3.What is the midpoint of the line joining (10, 6) and (12, 4)? (a) (5, 11) (b) (1, 1) (c) (11, 5) (d) (22, 10)
4. 4.In which quadrant does the point (6, −7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
5. 5.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
6. 6.What is the midpoint of the line joining (8, 1) and (12, 3)? (a) (2, 10) (b) (2, 1) (c) (10, 2) (d) (20, 4)
7. 7.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
8. 8.What is the midpoint of the line joining (8, 16) and (20, 6)? (a) (14, 11) (b) (11, 14) (c) (6, 5) (d) (28, 22)
9. 9.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
10. 10.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
11. 11.In which quadrant does the point (1, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
12. 12.What is the midpoint of the line joining (0, 10) and (4, 0)? (a) (4, 10) (b) (2, 5) (c) (5, 2) (d) (3, 5)
13. 13.In which quadrant does the point (−2, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
14. 14.What is the midpoint of the line joining (3, 16) and (7, 4)? (a) (2, 6) (b) (10, 5) (c) (5, 10) (d) (10, 20)
15. 15.What is the distance between the points (6, 15) and (11, 3)? (a) 14 (b) 169 (c) 17 (d) 13
16. 16.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
17. 17.What is the midpoint of the line joining (2, 1) and (6, 7)? (a) (2, 3) (b) (5, 4) (c) (8, 8) (d) (4, 4)
18. 18.What is the distance between the points (1, 13) and (16, 5)? (a) 18 (b) 17 (c) 289 (d) 23
19. 19.What is the distance between the points (8, 8) and (20, 3)? (a) 14 (b) 13 (c) 17 (d) 169
20. 20.In which quadrant does the point (7, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
21. 21.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
22. 22.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 14 (d) 169
23. 23.What is the distance between the points (0, 4) and (9, 16)? (a) 16 (b) 225 (c) 21 (d) 15
24. 24.In which quadrant does the point (−6, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
25. 25.What is the distance between the points (8, 0) and (23, 8)? (a) 17 (b) 18 (c) 289 (d) 23
26. 26.What is the midpoint of the line joining (1, 6) and (5, 8)? (a) (7, 3) (b) (2, 1) (c) (6, 14) (d) (3, 7)
27. 27.What is the midpoint of the line joining (1, 5) and (3, 9)? (a) (7, 2) (b) (4, 14) (c) (2, 7) (d) (1, 2)
28. 28.In which quadrant does the point (2, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
29. 29.What is the distance between the points (9, 8) and (21, 17)? (a) 21 (b) 16 (c) 225 (d) 15
30. 30.In which quadrant does the point (−1, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
31. 31.In which quadrant does the point (9, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
32. 32.What is the midpoint of the line joining (5, 12) and (7, 4)? (a) (6, 8) (b) (1, 4) (c) (8, 6) (d) (12, 16)
33. 33.What is the distance between the points (8, 1) and (20, 17)? (a) 21 (b) 400 (c) 20 (d) 28
34. 34.What is the midpoint of the line joining (10, 0) and (20, 2)? (a) (5, 1) (b) (15, 1) (c) (1, 15) (d) (30, 2)
35. 35.What is the distance between the points (0, 1) and (12, 17)? (a) 28 (b) 400 (c) 20 (d) 21
36. 36.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
37. 37.What is the distance between the points (3, 8) and (8, 20)? (a) 17 (b) 14 (c) 13 (d) 169
38. 38.What is the midpoint of the line joining (10, 6) and (14, 4)? (a) (5, 12) (b) (2, 1) (c) (24, 10) (d) (12, 5)
39. 39.What is the distance between the points (6, 13) and (14, 7)? (a) 14 (b) 100 (c) 11 (d) 10
40. 40.What is the midpoint of the line joining (7, 4) and (9, 0)? (a) (2, 8) (b) (8, 2) (c) (1, 2) (d) (16, 4)

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