Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 81 · 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.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
2. 2.In which quadrant does the point (1, 5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
3. 3.What is the midpoint of the line joining (9, 4) and (15, 0)? (a) (3, 2) (b) (24, 4) (c) (12, 2) (d) (2, 12)
4. 4.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
5. 5.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
6. 6.What is the midpoint of the line joining (5, 10) and (17, 18)? (a) (22, 28) (b) (11, 14) (c) (6, 4) (d) (14, 11)
7. 7.What is the distance between the points (0, 5) and (5, 17)? (a) 14 (b) 169 (c) 13 (d) 17
8. 8.In which quadrant does the point (−3, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
9. 9.What is the distance between the points (6, 9) and (14, 3)? (a) 11 (b) 100 (c) 14 (d) 10
10. 10.What is the distance between the points (2, 15) and (10, 0)? (a) 289 (b) 17 (c) 18 (d) 23
11. 11.What is the midpoint of the line joining (0, 8) and (4, 16)? (a) (2, 4) (b) (12, 2) (c) (4, 24) (d) (2, 12)
12. 12.What is the midpoint of the line joining (5, 13) and (11, 3)? (a) (3, 5) (b) (16, 16) (c) (8, 8) (d) (9, 8)
13. 13.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
14. 14.What is the distance between the points (8, 17) and (13, 5)? (a) 17 (b) 14 (c) 13 (d) 169
15. 15.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
16. 16.What is the distance between the points (9, 10) and (21, 1)? (a) 21 (b) 225 (c) 16 (d) 15
17. 17.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
18. 18.What is the midpoint of the line joining (2, 1) and (8, 5)? (a) (10, 6) (b) (3, 2) (c) (5, 3) (d) (3, 5)
19. 19.What is the midpoint of the line joining (7, 7) and (13, 13)? (a) (20, 20) (b) (11, 10) (c) (3, 3) (d) (10, 10)
20. 20.What is the midpoint of the line joining (6, 7) and (18, 9)? (a) (24, 16) (b) (6, 1) (c) (12, 8) (d) (8, 12)
21. 21.In which quadrant does the point (−7, −5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
22. 22.What is the distance between the points (6, 5) and (11, 17)? (a) 14 (b) 17 (c) 13 (d) 169
23. 23.What is the distance between the points (3, 5) and (12, 17)? (a) 21 (b) 15 (c) 225 (d) 16
24. 24.What is the midpoint of the line joining (9, 8) and (15, 14)? (a) (24, 22) (b) (11, 12) (c) (3, 3) (d) (12, 11)
25. 25.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
26. 26.In which quadrant does the point (6, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
27. 27.What is the distance between the points (9, 5) and (24, 13)? (a) 289 (b) 23 (c) 18 (d) 17
28. 28.What is the distance between the points (4, 15) and (28, 8)? (a) 625 (b) 25 (c) 31 (d) 26
29. 29.What is the distance between the points (8, 12) and (24, 0)? (a) 400 (b) 28 (c) 20 (d) 21
30. 30.What is the midpoint of the line joining (4, 2) and (12, 8)? (a) (5, 8) (b) (8, 5) (c) (4, 3) (d) (16, 10)
31. 31.What is the midpoint of the line joining (4, 1) and (6, 9)? (a) (6, 5) (b) (10, 10) (c) (1, 4) (d) (5, 5)
32. 32.What is the midpoint of the line joining (2, 9) and (8, 19)? (a) (5, 14) (b) (3, 5) (c) (14, 5) (d) (10, 28)
33. 33.What is the midpoint of the line joining (2, 4) and (12, 6)? (a) (5, 7) (b) (5, 1) (c) (14, 10) (d) (7, 5)
34. 34.What is the distance between the points (2, 8) and (14, 24)? (a) 21 (b) 28 (c) 400 (d) 20
35. 35.In which quadrant does the point (1, 7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
36. 36.What is the midpoint of the line joining (4, 2) and (16, 12)? (a) (7, 10) (b) (10, 7) (c) (20, 14) (d) (6, 5)
37. 37.What is the midpoint of the line joining (8, 1) and (16, 7)? (a) (24, 8) (b) (4, 3) (c) (12, 4) (d) (4, 12)
38. 38.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
39. 39.What is the midpoint of the line joining (0, 6) and (10, 18)? (a) (10, 24) (b) (12, 5) (c) (5, 12) (d) (5, 6)
40. 40.What is the distance between the points (8, 8) and (23, 0)? (a) 289 (b) 23 (c) 17 (d) 18

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