Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 378 · 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 (1, 6) and (17, 18)? (a) 400 (b) 20 (c) 21 (d) 28
2. 2.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
3. 3.What is the midpoint of the line joining (1, 10) and (3, 14)? (a) (2, 12) (b) (12, 2) (c) (1, 2) (d) (4, 24)
4. 4.What is the midpoint of the line joining (2, 1) and (8, 5)? (a) (5, 3) (b) (3, 2) (c) (10, 6) (d) (3, 5)
5. 5.What is the midpoint of the line joining (3, 5) and (5, 1)? (a) (1, 2) (b) (4, 3) (c) (3, 4) (d) (8, 6)
6. 6.What is the midpoint of the line joining (8, 17) and (12, 7)? (a) (20, 24) (b) (2, 5) (c) (10, 12) (d) (12, 10)
7. 7.What is the distance between the points (7, 1) and (23, 13)? (a) 28 (b) 400 (c) 20 (d) 21
8. 8.What is the midpoint of the line joining (9, 15) and (13, 3)? (a) (9, 11) (b) (22, 18) (c) (11, 9) (d) (2, 6)
9. 9.In which quadrant does the point (−1, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
10. 10.What is the midpoint of the line joining (2, 12) and (10, 4)? (a) (6, 8) (b) (8, 6) (c) (4, 4) (d) (12, 16)
11. 11.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
12. 12.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
13. 13.In which quadrant does the point (8, −2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
14. 14.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
15. 15.In which quadrant does the point (6, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
16. 16.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
17. 17.What is the distance between the points (0, 2) and (15, 10)? (a) 289 (b) 18 (c) 23 (d) 17
18. 18.What is the midpoint of the line joining (8, 0) and (12, 10)? (a) (5, 10) (b) (20, 10) (c) (2, 5) (d) (10, 5)
19. 19.In which quadrant does the point (5, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
20. 20.What is the midpoint of the line joining (9, 14) and (15, 10)? (a) (24, 24) (b) (3, 2) (c) (12, 12) (d) (13, 12)
21. 21.What is the midpoint of the line joining (10, 8) and (12, 4)? (a) (11, 6) (b) (22, 12) (c) (6, 11) (d) (1, 2)
22. 22.What is the distance between the points (1, 3) and (10, 15)? (a) 16 (b) 21 (c) 15 (d) 225
23. 23.In which quadrant does the point (−7, −9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
24. 24.What is the distance between the points (4, 2) and (16, 11)? (a) 15 (b) 16 (c) 21 (d) 225
25. 25.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
26. 26.What is the midpoint of the line joining (7, 13) and (19, 1)? (a) (7, 13) (b) (13, 7) (c) (6, 6) (d) (26, 14)
27. 27.What is the midpoint of the line joining (4, 3) and (14, 7)? (a) (5, 2) (b) (18, 10) (c) (5, 9) (d) (9, 5)
28. 28.What is the distance between the points (4, 3) and (16, 19)? (a) 20 (b) 21 (c) 400 (d) 28
29. 29.In which quadrant does the point (−6, 1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
30. 30.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
31. 31.What is the midpoint of the line joining (4, 9) and (6, 15)? (a) (5, 12) (b) (12, 5) (c) (10, 24) (d) (1, 3)
32. 32.What is the midpoint of the line joining (9, 0) and (19, 6)? (a) (5, 3) (b) (28, 6) (c) (3, 14) (d) (14, 3)
33. 33.What is the distance between the points (8, 1) and (13, 13)? (a) 13 (b) 14 (c) 169 (d) 17
34. 34.In which quadrant does the point (−8, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
35. 35.In which quadrant does the point (−3, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
36. 36.What is the distance between the points (6, 20) and (22, 8)? (a) 20 (b) 400 (c) 28 (d) 21
37. 37.What is the midpoint of the line joining (3, 5) and (7, 3)? (a) (4, 5) (b) (2, 1) (c) (10, 8) (d) (5, 4)
38. 38.What is the midpoint of the line joining (0, 4) and (6, 12)? (a) (6, 16) (b) (8, 3) (c) (3, 4) (d) (3, 8)
39. 39.What is the distance between the points (7, 1) and (15, 16)? (a) 23 (b) 18 (c) 289 (d) 17
40. 40.What is the distance between the points (9, 7) and (18, 19)? (a) 21 (b) 16 (c) 15 (d) 225

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