Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 663 · 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 (−2, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
2. 2.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
3. 3.In which quadrant does the point (1, −5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
4. 4.What is the midpoint of the line joining (6, 12) and (12, 0)? (a) (18, 12) (b) (3, 6) (c) (6, 9) (d) (9, 6)
5. 5.In which quadrant does the point (−1, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
7. 7.What is the midpoint of the line joining (6, 9) and (18, 7)? (a) (6, 1) (b) (24, 16) (c) (8, 12) (d) (12, 8)
8. 8.What is the midpoint of the line joining (4, 5) and (8, 13)? (a) (9, 6) (b) (2, 4) (c) (12, 18) (d) (6, 9)
9. 9.What is the midpoint of the line joining (4, 3) and (16, 5)? (a) (4, 10) (b) (6, 1) (c) (10, 4) (d) (20, 8)
10. 10.What is the midpoint of the line joining (1, 8) and (3, 6)? (a) (4, 14) (b) (2, 7) (c) (1, 1) (d) (7, 2)
11. 11.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
12. 12.In which quadrant does the point (2, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
13. 13.What is the midpoint of the line joining (10, 11) and (12, 1)? (a) (6, 11) (b) (11, 6) (c) (1, 5) (d) (22, 12)
14. 14.What is the midpoint of the line joining (5, 11) and (9, 1)? (a) (2, 5) (b) (7, 6) (c) (14, 12) (d) (6, 7)
15. 15.What is the distance between the points (8, 11) and (11, 7)? (a) 7 (b) 6 (c) 25 (d) 5
16. 16.What is the midpoint of the line joining (3, 14) and (11, 10)? (a) (12, 7) (b) (14, 24) (c) (7, 12) (d) (4, 2)
17. 17.What is the midpoint of the line joining (1, 3) and (5, 1)? (a) (3, 2) (b) (6, 4) (c) (2, 1) (d) (2, 3)
18. 18.What is the midpoint of the line joining (5, 2) and (9, 4)? (a) (2, 1) (b) (3, 7) (c) (14, 6) (d) (7, 3)
19. 19.What is the midpoint of the line joining (6, 7) and (14, 5)? (a) (20, 12) (b) (6, 10) (c) (4, 1) (d) (10, 6)
20. 20.What is the distance between the points (8, 1) and (15, 25)? (a) 26 (b) 31 (c) 625 (d) 25
21. 21.What is the distance between the points (0, 7) and (15, 15)? (a) 23 (b) 289 (c) 17 (d) 18
22. 22.What is the midpoint of the line joining (6, 0) and (18, 4)? (a) (2, 12) (b) (24, 4) (c) (6, 2) (d) (12, 2)
23. 23.In which quadrant does the point (−9, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
24. 24.What is the midpoint of the line joining (0, 10) and (6, 14)? (a) (3, 12) (b) (6, 24) (c) (3, 2) (d) (12, 3)
25. 25.What is the midpoint of the line joining (6, 7) and (18, 19)? (a) (12, 13) (b) (13, 12) (c) (6, 6) (d) (24, 26)
26. 26.What is the distance between the points (0, 11) and (12, 6)? (a) 169 (b) 14 (c) 17 (d) 13
27. 27.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
28. 28.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
29. 29.What is the distance between the points (8, 15) and (17, 3)? (a) 16 (b) 15 (c) 21 (d) 225
30. 30.What is the midpoint of the line joining (1, 11) and (13, 9)? (a) (10, 7) (b) (7, 10) (c) (14, 20) (d) (6, 1)
31. 31.What is the distance between the points (2, 10) and (6, 7)? (a) 5 (b) 25 (c) 7 (d) 6
32. 32.What is the distance between the points (7, 18) and (12, 6)? (a) 14 (b) 17 (c) 169 (d) 13
33. 33.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
34. 34.What is the distance between the points (1, 5) and (13, 0)? (a) 169 (b) 14 (c) 17 (d) 13
35. 35.What is the midpoint of the line joining (4, 1) and (6, 9)? (a) (6, 5) (b) (1, 4) (c) (5, 5) (d) (10, 10)
36. 36.In which quadrant does the point (6, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
37. 37.What is the distance between the points (2, 7) and (10, 1)? (a) 100 (b) 14 (c) 11 (d) 10
38. 38.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
39. 39.What is the midpoint of the line joining (7, 10) and (19, 22)? (a) (6, 6) (b) (16, 13) (c) (26, 32) (d) (13, 16)
40. 40.In which quadrant does the point (8, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant

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