Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 465 · 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.In which quadrant does the point (−3, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
2. 2.What is the midpoint of the line joining (3, 18) and (7, 8)? (a) (2, 5) (b) (13, 5) (c) (5, 13) (d) (10, 26)
3. 3.In which quadrant does the point (5, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
4. 4.What is the distance between the points (3, 7) and (12, 19)? (a) 21 (b) 15 (c) 16 (d) 225
5. 5.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
6. 6.What is the distance between the points (5, 10) and (8, 6)? (a) 6 (b) 5 (c) 7 (d) 25
7. 7.In which quadrant does the point (9, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
8. 8.What is the midpoint of the line joining (9, 5) and (21, 17)? (a) (30, 22) (b) (15, 11) (c) (6, 6) (d) (11, 15)
9. 9.What is the distance between the points (3, 6) and (11, 0)? (a) 11 (b) 14 (c) 10 (d) 100
10. 10.What is the distance between the points (4, 18) and (13, 6)? (a) 15 (b) 21 (c) 225 (d) 16
11. 11.In which quadrant does the point (−9, −4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
12. 12.In which quadrant does the point (4, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
13. 13.What is the midpoint of the line joining (8, 6) and (10, 0)? (a) (1, 3) (b) (9, 3) (c) (18, 6) (d) (3, 9)
14. 14.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
15. 15.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
16. 16.What is the midpoint of the line joining (3, 19) and (13, 7)? (a) (16, 26) (b) (8, 13) (c) (5, 6) (d) (13, 8)
17. 17.What is the distance between the points (7, 13) and (19, 8)? (a) 17 (b) 14 (c) 13 (d) 169
18. 18.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
19. 19.What is the midpoint of the line joining (8, 7) and (14, 3)? (a) (3, 2) (b) (22, 10) (c) (5, 11) (d) (11, 5)
20. 20.What is the distance between the points (7, 5) and (19, 14)? (a) 225 (b) 21 (c) 15 (d) 16
21. 21.What is the midpoint of the line joining (1, 8) and (13, 18)? (a) (7, 13) (b) (6, 5) (c) (13, 7) (d) (14, 26)
22. 22.What is the distance between the points (5, 1) and (11, 9)? (a) 14 (b) 10 (c) 11 (d) 100
23. 23.What is the distance between the points (7, 9) and (19, 18)? (a) 16 (b) 225 (c) 21 (d) 15
24. 24.What is the distance between the points (3, 11) and (11, 5)? (a) 100 (b) 14 (c) 10 (d) 11
25. 25.What is the midpoint of the line joining (8, 5) and (16, 17)? (a) (4, 6) (b) (12, 11) (c) (11, 12) (d) (24, 22)
26. 26.In which quadrant does the point (7, −5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
27. 27.What is the midpoint of the line joining (2, 1) and (14, 13)? (a) (16, 14) (b) (8, 7) (c) (7, 8) (d) (6, 6)
28. 28.What is the distance between the points (6, 19) and (11, 7)? (a) 17 (b) 169 (c) 14 (d) 13
29. 29.What is the distance between the points (2, 1) and (6, 4)? (a) 25 (b) 7 (c) 6 (d) 5
30. 30.What is the distance between the points (7, 2) and (19, 7)? (a) 169 (b) 17 (c) 13 (d) 14
31. 31.In which quadrant does the point (3, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
32. 32.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
33. 33.In which quadrant does the point (−8, −5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
34. 34.What is the midpoint of the line joining (1, 10) and (11, 14)? (a) (5, 2) (b) (12, 24) (c) (12, 6) (d) (6, 12)
35. 35.In which quadrant does the point (−6, −1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
36. 36.What is the midpoint of the line joining (0, 13) and (10, 7)? (a) (5, 10) (b) (5, 3) (c) (10, 20) (d) (10, 5)
37. 37.What is the midpoint of the line joining (8, 8) and (10, 10)? (a) (9, 9) (b) (1, 1) (c) (10, 9) (d) (18, 18)
38. 38.In which quadrant does the point (−7, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
39. 39.What is the midpoint of the line joining (9, 8) and (11, 18)? (a) (10, 13) (b) (1, 5) (c) (13, 10) (d) (20, 26)
40. 40.In which quadrant does the point (−5, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant

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