Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 184 · 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 (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
2. 2.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
3. 3.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
4. 4.What is the distance between the points (9, 7) and (14, 19)? (a) 17 (b) 169 (c) 13 (d) 14
5. 5.What is the distance between the points (6, 7) and (18, 2)? (a) 13 (b) 14 (c) 17 (d) 169
6. 6.What is the midpoint of the line joining (1, 4) and (9, 6)? (a) (4, 1) (b) (10, 10) (c) (5, 5) (d) (6, 5)
7. 7.What is the distance between the points (3, 20) and (8, 8)? (a) 14 (b) 13 (c) 169 (d) 17
8. 8.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
9. 9.In which quadrant does the point (−4, 9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
10. 10.What is the midpoint of the line joining (10, 8) and (22, 2)? (a) (32, 10) (b) (5, 16) (c) (6, 3) (d) (16, 5)
11. 11.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
12. 12.What is the midpoint of the line joining (1, 10) and (11, 6)? (a) (5, 2) (b) (12, 16) (c) (6, 8) (d) (8, 6)
13. 13.What is the midpoint of the line joining (1, 4) and (3, 2)? (a) (1, 1) (b) (4, 6) (c) (2, 3) (d) (3, 2)
14. 14.In which quadrant does the point (−5, −3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
15. 15.What is the midpoint of the line joining (3, 10) and (9, 12)? (a) (12, 22) (b) (3, 1) (c) (11, 6) (d) (6, 11)
16. 16.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
17. 17.What is the distance between the points (4, 10) and (7, 6)? (a) 25 (b) 6 (c) 7 (d) 5
18. 18.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
19. 19.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
20. 20.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
21. 21.In which quadrant does the point (−2, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
22. 22.What is the distance between the points (0, 16) and (5, 4)? (a) 17 (b) 13 (c) 14 (d) 169
23. 23.In which quadrant does the point (−7, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
24. 24.What is the distance between the points (2, 7) and (11, 19)? (a) 21 (b) 16 (c) 225 (d) 15
25. 25.What is the midpoint of the line joining (4, 6) and (14, 14)? (a) (5, 4) (b) (9, 10) (c) (18, 20) (d) (10, 9)
26. 26.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
27. 27.What is the distance between the points (0, 4) and (24, 11)? (a) 625 (b) 26 (c) 31 (d) 25
28. 28.What is the distance between the points (1, 7) and (9, 13)? (a) 10 (b) 14 (c) 100 (d) 11
29. 29.What is the distance between the points (1, 19) and (9, 4)? (a) 17 (b) 18 (c) 289 (d) 23
30. 30.What is the distance between the points (2, 14) and (18, 2)? (a) 28 (b) 21 (c) 400 (d) 20
31. 31.What is the distance between the points (0, 4) and (8, 10)? (a) 11 (b) 10 (c) 14 (d) 100
32. 32.What is the distance between the points (2, 21) and (14, 5)? (a) 28 (b) 21 (c) 400 (d) 20
33. 33.What is the distance between the points (5, 4) and (8, 0)? (a) 7 (b) 25 (c) 6 (d) 5
34. 34.What is the midpoint of the line joining (0, 9) and (10, 15)? (a) (5, 12) (b) (12, 5) (c) (10, 24) (d) (5, 3)
35. 35.What is the midpoint of the line joining (3, 8) and (9, 12)? (a) (12, 20) (b) (3, 2) (c) (10, 6) (d) (6, 10)
36. 36.What is the distance between the points (7, 4) and (23, 16)? (a) 400 (b) 20 (c) 28 (d) 21
37. 37.What is the distance between the points (8, 4) and (16, 10)? (a) 14 (b) 11 (c) 10 (d) 100
38. 38.What is the midpoint of the line joining (1, 11) and (3, 3)? (a) (2, 7) (b) (4, 14) (c) (1, 4) (d) (7, 2)
39. 39.What is the midpoint of the line joining (1, 10) and (5, 18)? (a) (6, 28) (b) (2, 4) (c) (14, 3) (d) (3, 14)
40. 40.What is the midpoint of the line joining (9, 12) and (13, 4)? (a) (2, 4) (b) (22, 16) (c) (8, 11) (d) (11, 8)

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