Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 529 · 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, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
2. 2.What is the distance between the points (8, 2) and (11, 6)? (a) 6 (b) 5 (c) 7 (d) 25
3. 3.What is the midpoint of the line joining (2, 13) and (6, 3)? (a) (4, 8) (b) (8, 4) (c) (8, 16) (d) (2, 5)
4. 4.In which quadrant does the point (−8, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
5. 5.What is the midpoint of the line joining (4, 3) and (12, 5)? (a) (4, 8) (b) (16, 8) (c) (4, 1) (d) (8, 4)
6. 6.What is the midpoint of the line joining (1, 5) and (5, 13)? (a) (9, 3) (b) (6, 18) (c) (3, 9) (d) (2, 4)
7. 7.In which quadrant does the point (−1, 2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
8. 8.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
9. 9.What is the distance between the points (6, 11) and (18, 6)? (a) 17 (b) 169 (c) 13 (d) 14
10. 10.What is the distance between the points (2, 0) and (6, 3)? (a) 25 (b) 7 (c) 6 (d) 5
11. 11.What is the midpoint of the line joining (1, 11) and (5, 7)? (a) (6, 18) (b) (3, 9) (c) (9, 3) (d) (2, 2)
12. 12.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
13. 13.In which quadrant does the point (2, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
14. 14.What is the midpoint of the line joining (6, 1) and (16, 13)? (a) (11, 7) (b) (7, 11) (c) (5, 6) (d) (22, 14)
15. 15.In which quadrant does the point (3, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
16. 16.In which quadrant does the point (1, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
17. 17.What is the midpoint of the line joining (10, 5) and (12, 13)? (a) (9, 11) (b) (1, 4) (c) (22, 18) (d) (11, 9)
18. 18.What is the midpoint of the line joining (2, 15) and (4, 3)? (a) (3, 9) (b) (6, 18) (c) (9, 3) (d) (1, 6)
19. 19.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
20. 20.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
21. 21.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
22. 22.In which quadrant does the point (8, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
23. 23.In which quadrant does the point (−3, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
24. 24.What is the distance between the points (9, 7) and (17, 1)? (a) 10 (b) 11 (c) 100 (d) 14
25. 25.What is the distance between the points (3, 12) and (8, 0)? (a) 17 (b) 169 (c) 14 (d) 13
26. 26.What is the midpoint of the line joining (8, 5) and (18, 3)? (a) (13, 4) (b) (26, 8) (c) (5, 1) (d) (4, 13)
27. 27.In which quadrant does the point (−7, 6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
28. 28.What is the midpoint of the line joining (3, 5) and (15, 13)? (a) (18, 18) (b) (6, 4) (c) (10, 9) (d) (9, 9)
29. 29.What is the distance between the points (5, 1) and (17, 17)? (a) 28 (b) 21 (c) 20 (d) 400
30. 30.In which quadrant does the point (−1, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
31. 31.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
32. 32.What is the distance between the points (1, 5) and (17, 17)? (a) 400 (b) 21 (c) 28 (d) 20
33. 33.What is the distance between the points (6, 14) and (30, 7)? (a) 26 (b) 625 (c) 31 (d) 25
34. 34.What is the distance between the points (8, 14) and (20, 9)? (a) 169 (b) 17 (c) 13 (d) 14
35. 35.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
36. 36.What is the midpoint of the line joining (1, 12) and (3, 2)? (a) (7, 2) (b) (1, 5) (c) (2, 7) (d) (4, 14)
37. 37.In which quadrant does the point (−4, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
38. 38.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
39. 39.What is the midpoint of the line joining (2, 14) and (6, 4)? (a) (2, 5) (b) (4, 9) (c) (8, 18) (d) (9, 4)
40. 40.What is the distance between the points (6, 14) and (18, 5)? (a) 21 (b) 225 (c) 15 (d) 16

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