Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 80 · 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 (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
2. 2.What is the midpoint of the line joining (1, 1) and (11, 5)? (a) (6, 3) (b) (3, 6) (c) (5, 2) (d) (12, 6)
3. 3.In which quadrant does the point (−6, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
4. 4.In which quadrant does the point (3, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
5. 5.In which quadrant does the point (9, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
6. 6.What is the distance between the points (1, 11) and (16, 3)? (a) 18 (b) 23 (c) 17 (d) 289
7. 7.What is the midpoint of the line joining (0, 14) and (8, 2)? (a) (8, 16) (b) (4, 8) (c) (8, 4) (d) (4, 6)
8. 8.What is the distance between the points (0, 5) and (8, 11)? (a) 10 (b) 100 (c) 11 (d) 14
9. 9.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
10. 10.What is the midpoint of the line joining (2, 9) and (12, 21)? (a) (15, 7) (b) (7, 15) (c) (14, 30) (d) (5, 6)
11. 11.What is the distance between the points (9, 15) and (17, 0)? (a) 23 (b) 18 (c) 17 (d) 289
12. 12.What is the midpoint of the line joining (0, 2) and (10, 10)? (a) (6, 5) (b) (5, 6) (c) (5, 4) (d) (10, 12)
13. 13.What is the midpoint of the line joining (0, 7) and (8, 11)? (a) (4, 9) (b) (4, 2) (c) (8, 18) (d) (9, 4)
14. 14.What is the distance between the points (7, 6) and (19, 11)? (a) 169 (b) 17 (c) 14 (d) 13
15. 15.What is the distance between the points (9, 9) and (17, 3)? (a) 10 (b) 100 (c) 11 (d) 14
16. 16.What is the distance between the points (0, 14) and (5, 2)? (a) 169 (b) 17 (c) 13 (d) 14
17. 17.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
18. 18.What is the distance between the points (2, 9) and (17, 1)? (a) 18 (b) 289 (c) 17 (d) 23
19. 19.In which quadrant does the point (6, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
20. 20.What is the distance between the points (6, 2) and (13, 26)? (a) 26 (b) 625 (c) 31 (d) 25
21. 21.What is the midpoint of the line joining (6, 1) and (16, 7)? (a) (11, 4) (b) (4, 11) (c) (5, 3) (d) (22, 8)
22. 22.What is the midpoint of the line joining (6, 7) and (8, 17)? (a) (7, 12) (b) (1, 5) (c) (12, 7) (d) (14, 24)
23. 23.What is the distance between the points (1, 6) and (9, 21)? (a) 17 (b) 18 (c) 289 (d) 23
24. 24.What is the distance between the points (2, 12) and (7, 0)? (a) 17 (b) 169 (c) 14 (d) 13
25. 25.What is the distance between the points (4, 2) and (13, 14)? (a) 21 (b) 15 (c) 225 (d) 16
26. 26.What is the distance between the points (4, 4) and (7, 0)? (a) 6 (b) 25 (c) 5 (d) 7
27. 27.In which quadrant does the point (−5, 8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
28. 28.What is the distance between the points (0, 2) and (8, 17)? (a) 18 (b) 289 (c) 23 (d) 17
29. 29.In which quadrant does the point (6, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
30. 30.In which quadrant does the point (−7, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
31. 31.In which quadrant does the point (8, 5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
32. 32.What is the distance between the points (9, 6) and (15, 14)? (a) 10 (b) 14 (c) 11 (d) 100
33. 33.What is the midpoint of the line joining (7, 7) and (15, 19)? (a) (13, 11) (b) (11, 13) (c) (4, 6) (d) (22, 26)
34. 34.What is the midpoint of the line joining (7, 6) and (15, 16)? (a) (11, 11) (b) (12, 11) (c) (22, 22) (d) (4, 5)
35. 35.What is the distance between the points (2, 14) and (26, 7)? (a) 26 (b) 25 (c) 625 (d) 31
36. 36.What is the midpoint of the line joining (10, 17) and (14, 9)? (a) (24, 26) (b) (12, 13) (c) (2, 4) (d) (13, 12)
37. 37.In which quadrant does the point (−8, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
38. 38.In which quadrant does the point (3, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
39. 39.What is the distance between the points (0, 5) and (12, 10)? (a) 14 (b) 13 (c) 17 (d) 169
40. 40.In which quadrant does the point (−1, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant

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