Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 93 · 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 (0, 11) and (6, 7)? (a) (9, 3) (b) (3, 9) (c) (6, 18) (d) (3, 2)
2. 2.In which quadrant does the point (6, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
3. 3.In which quadrant does the point (−5, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
4. 4.What is the midpoint of the line joining (0, 2) and (2, 12)? (a) (2, 14) (b) (1, 7) (c) (7, 1) (d) (1, 5)
5. 5.What is the midpoint of the line joining (7, 1) and (19, 3)? (a) (13, 2) (b) (6, 1) (c) (2, 13) (d) (26, 4)
6. 6.What is the distance between the points (9, 2) and (12, 6)? (a) 5 (b) 7 (c) 6 (d) 25
7. 7.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
8. 8.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
9. 9.What is the midpoint of the line joining (3, 8) and (13, 14)? (a) (16, 22) (b) (11, 8) (c) (8, 11) (d) (5, 3)
10. 10.What is the midpoint of the line joining (10, 0) and (18, 2)? (a) (28, 2) (b) (4, 1) (c) (1, 14) (d) (14, 1)
11. 11.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
12. 12.What is the midpoint of the line joining (2, 9) and (8, 17)? (a) (3, 4) (b) (13, 5) (c) (5, 13) (d) (10, 26)
13. 13.What is the midpoint of the line joining (0, 3) and (8, 5)? (a) (4, 1) (b) (8, 8) (c) (4, 4) (d) (5, 4)
14. 14.What is the distance between the points (2, 4) and (18, 16)? (a) 21 (b) 20 (c) 400 (d) 28
15. 15.What is the midpoint of the line joining (1, 15) and (9, 3)? (a) (4, 6) (b) (10, 18) (c) (9, 5) (d) (5, 9)
16. 16.What is the distance between the points (1, 0) and (7, 8)? (a) 11 (b) 100 (c) 14 (d) 10
17. 17.What is the midpoint of the line joining (1, 7) and (5, 9)? (a) (2, 1) (b) (8, 3) (c) (6, 16) (d) (3, 8)
18. 18.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
19. 19.What is the distance between the points (7, 25) and (14, 1)? (a) 31 (b) 26 (c) 625 (d) 25
20. 20.In which quadrant does the point (7, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
21. 21.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
22. 22.What is the midpoint of the line joining (5, 14) and (7, 2)? (a) (6, 8) (b) (1, 6) (c) (8, 6) (d) (12, 16)
23. 23.In which quadrant does the point (6, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
24. 24.What is the midpoint of the line joining (2, 12) and (6, 6)? (a) (9, 4) (b) (4, 9) (c) (8, 18) (d) (2, 3)
25. 25.What is the distance between the points (3, 8) and (11, 23)? (a) 23 (b) 289 (c) 17 (d) 18
26. 26.What is the midpoint of the line joining (10, 5) and (18, 3)? (a) (28, 8) (b) (4, 1) (c) (14, 4) (d) (4, 14)
27. 27.In which quadrant does the point (3, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
28. 28.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
29. 29.What is the midpoint of the line joining (0, 14) and (10, 2)? (a) (5, 8) (b) (5, 6) (c) (8, 5) (d) (10, 16)
30. 30.What is the midpoint of the line joining (7, 14) and (9, 4)? (a) (9, 8) (b) (1, 5) (c) (16, 18) (d) (8, 9)
31. 31.In which quadrant does the point (−1, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
32. 32.In which quadrant does the point (9, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
33. 33.What is the distance between the points (5, 14) and (20, 6)? (a) 18 (b) 289 (c) 23 (d) 17
34. 34.What is the distance between the points (2, 9) and (5, 5)? (a) 5 (b) 6 (c) 7 (d) 25
35. 35.In which quadrant does the point (−9, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
36. 36.In which quadrant does the point (1, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
37. 37.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
38. 38.What is the distance between the points (9, 14) and (21, 9)? (a) 169 (b) 17 (c) 13 (d) 14
39. 39.What is the midpoint of the line joining (0, 3) and (2, 9)? (a) (6, 1) (b) (2, 12) (c) (1, 3) (d) (1, 6)
40. 40.In which quadrant does the point (6, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant

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