Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 112 · 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 (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
2. 2.What is the distance between the points (3, 1) and (8, 13)? (a) 169 (b) 14 (c) 17 (d) 13
3. 3.What is the midpoint of the line joining (9, 8) and (19, 6)? (a) (14, 7) (b) (28, 14) (c) (7, 14) (d) (5, 1)
4. 4.What is the midpoint of the line joining (0, 9) and (2, 13)? (a) (2, 22) (b) (1, 2) (c) (1, 11) (d) (11, 1)
5. 5.In which quadrant does the point (9, −3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
6. 6.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
7. 7.In which quadrant does the point (4, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
8. 8.What is the midpoint of the line joining (3, 2) and (5, 14)? (a) (8, 16) (b) (1, 6) (c) (4, 8) (d) (8, 4)
9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
10. 10.In which quadrant does the point (−4, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
11. 11.What is the distance between the points (8, 14) and (20, 9)? (a) 17 (b) 169 (c) 14 (d) 13
12. 12.In which quadrant does the point (6, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
13. 13.What is the midpoint of the line joining (8, 3) and (12, 9)? (a) (10, 6) (b) (20, 12) (c) (2, 3) (d) (6, 10)
14. 14.What is the midpoint of the line joining (6, 5) and (14, 7)? (a) (20, 12) (b) (10, 6) (c) (4, 1) (d) (6, 10)
15. 15.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
16. 16.What is the midpoint of the line joining (4, 18) and (8, 8)? (a) (6, 13) (b) (2, 5) (c) (13, 6) (d) (12, 26)
17. 17.What is the midpoint of the line joining (4, 3) and (6, 15)? (a) (10, 18) (b) (5, 9) (c) (9, 5) (d) (1, 6)
18. 18.What is the midpoint of the line joining (4, 12) and (8, 10)? (a) (2, 1) (b) (6, 11) (c) (11, 6) (d) (12, 22)
19. 19.What is the midpoint of the line joining (2, 0) and (6, 10)? (a) (2, 5) (b) (4, 5) (c) (8, 10) (d) (5, 4)
20. 20.What is the midpoint of the line joining (3, 3) and (7, 11)? (a) (7, 5) (b) (5, 7) (c) (10, 14) (d) (2, 4)
21. 21.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
22. 22.What is the distance between the points (8, 8) and (12, 11)? (a) 25 (b) 7 (c) 5 (d) 6
23. 23.What is the midpoint of the line joining (10, 7) and (16, 19)? (a) (13, 13) (b) (14, 13) (c) (26, 26) (d) (3, 6)
24. 24.What is the distance between the points (0, 8) and (7, 32)? (a) 31 (b) 625 (c) 26 (d) 25
25. 25.What is the midpoint of the line joining (7, 3) and (19, 5)? (a) (26, 8) (b) (6, 1) (c) (13, 4) (d) (4, 13)
26. 26.What is the distance between the points (6, 16) and (22, 4)? (a) 21 (b) 400 (c) 20 (d) 28
27. 27.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
28. 28.In which quadrant does the point (−9, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
29. 29.What is the midpoint of the line joining (1, 0) and (7, 10)? (a) (3, 5) (b) (4, 5) (c) (5, 4) (d) (8, 10)
30. 30.What is the midpoint of the line joining (10, 9) and (20, 19)? (a) (15, 14) (b) (5, 5) (c) (30, 28) (d) (14, 15)
31. 31.In which quadrant does the point (−9, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
32. 32.In which quadrant does the point (−8, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
33. 33.In which quadrant does the point (1, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
34. 34.What is the midpoint of the line joining (6, 9) and (8, 13)? (a) (11, 7) (b) (7, 11) (c) (1, 2) (d) (14, 22)
35. 35.In which quadrant does the point (1, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
36. 36.What is the midpoint of the line joining (9, 1) and (17, 9)? (a) (13, 5) (b) (26, 10) (c) (4, 4) (d) (5, 13)
37. 37.What is the midpoint of the line joining (0, 7) and (10, 19)? (a) (13, 5) (b) (5, 6) (c) (10, 26) (d) (5, 13)
38. 38.What is the midpoint of the line joining (9, 5) and (19, 7)? (a) (28, 12) (b) (14, 6) (c) (5, 1) (d) (6, 14)
39. 39.What is the distance between the points (9, 3) and (21, 12)? (a) 225 (b) 15 (c) 21 (d) 16
40. 40.What is the distance between the points (8, 1) and (23, 9)? (a) 289 (b) 23 (c) 18 (d) 17

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