Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 580 · 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 midpoint of the line joining (8, 1) and (18, 9)? (a) (5, 13) (b) (5, 4) (c) (26, 10) (d) (13, 5)
2. 2.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
3. 3.What is the distance between the points (5, 1) and (10, 13)? (a) 169 (b) 17 (c) 14 (d) 13
4. 4.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
5. 5.In which quadrant does the point (3, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
6. 6.What is the distance between the points (0, 3) and (6, 11)? (a) 11 (b) 100 (c) 10 (d) 14
7. 7.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
8. 8.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
9. 9.What is the distance between the points (0, 8) and (12, 3)? (a) 17 (b) 169 (c) 14 (d) 13
10. 10.In which quadrant does the point (−3, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
11. 11.What is the distance between the points (4, 20) and (13, 8)? (a) 16 (b) 225 (c) 21 (d) 15
12. 12.What is the midpoint of the line joining (2, 8) and (10, 16)? (a) (4, 4) (b) (12, 6) (c) (12, 24) (d) (6, 12)
13. 13.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
14. 14.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
15. 15.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 21 (d) 225
16. 16.In which quadrant does the point (−1, −5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
17. 17.What is the midpoint of the line joining (1, 5) and (9, 9)? (a) (10, 14) (b) (4, 2) (c) (7, 5) (d) (5, 7)
18. 18.In which quadrant does the point (2, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
19. 19.In which quadrant does the point (−6, 7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
20. 20.In which quadrant does the point (−4, 7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
21. 21.In which quadrant does the point (−8, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
22. 22.What is the midpoint of the line joining (5, 7) and (11, 15)? (a) (16, 22) (b) (3, 4) (c) (11, 8) (d) (8, 11)
23. 23.What is the midpoint of the line joining (1, 6) and (5, 10)? (a) (3, 8) (b) (8, 3) (c) (6, 16) (d) (2, 2)
24. 24.In which quadrant does the point (−5, 4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
25. 25.What is the distance between the points (0, 7) and (16, 19)? (a) 20 (b) 21 (c) 400 (d) 28
26. 26.What is the distance between the points (3, 7) and (12, 19)? (a) 21 (b) 225 (c) 15 (d) 16
27. 27.In which quadrant does the point (−8, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
28. 28.What is the distance between the points (8, 1) and (11, 5)? (a) 25 (b) 5 (c) 6 (d) 7
29. 29.In which quadrant does the point (4, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
30. 30.What is the distance between the points (4, 10) and (16, 1)? (a) 15 (b) 225 (c) 16 (d) 21
31. 31.What is the distance between the points (1, 15) and (25, 8)? (a) 26 (b) 625 (c) 25 (d) 31
32. 32.What is the distance between the points (4, 15) and (16, 6)? (a) 16 (b) 225 (c) 21 (d) 15
33. 33.In which quadrant does the point (3, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
34. 34.In which quadrant does the point (3, −6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
35. 35.What is the midpoint of the line joining (3, 13) and (9, 3)? (a) (8, 6) (b) (3, 5) (c) (6, 8) (d) (12, 16)
36. 36.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
37. 37.What is the midpoint of the line joining (6, 6) and (14, 18)? (a) (10, 12) (b) (4, 6) (c) (12, 10) (d) (20, 24)
38. 38.What is the midpoint of the line joining (0, 4) and (10, 2)? (a) (3, 5) (b) (10, 6) (c) (5, 1) (d) (5, 3)
39. 39.What is the midpoint of the line joining (3, 11) and (9, 7)? (a) (9, 6) (b) (6, 9) (c) (3, 2) (d) (12, 18)
40. 40.What is the midpoint of the line joining (9, 6) and (11, 8)? (a) (1, 1) (b) (20, 14) (c) (7, 10) (d) (10, 7)

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