Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 350 · 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 (1, 4) and (13, 0)? (a) (2, 7) (b) (14, 4) (c) (6, 2) (d) (7, 2)
2. 2.What is the midpoint of the line joining (9, 14) and (21, 4)? (a) (30, 18) (b) (9, 15) (c) (6, 5) (d) (15, 9)
3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
4. 4.In which quadrant does the point (−7, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
5. 5.In which quadrant does the point (9, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
6. 6.What is the midpoint of the line joining (1, 4) and (7, 0)? (a) (2, 4) (b) (8, 4) (c) (3, 2) (d) (4, 2)
7. 7.What is the distance between the points (2, 1) and (7, 13)? (a) 17 (b) 14 (c) 169 (d) 13
8. 8.What is the midpoint of the line joining (10, 5) and (12, 9)? (a) (22, 14) (b) (1, 2) (c) (7, 11) (d) (11, 7)
9. 9.What is the distance between the points (7, 17) and (13, 9)? (a) 14 (b) 10 (c) 11 (d) 100
10. 10.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
11. 11.In which quadrant does the point (−9, 5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
12. 12.What is the distance between the points (7, 4) and (15, 10)? (a) 100 (b) 10 (c) 11 (d) 14
13. 13.In which quadrant does the point (4, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
14. 14.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
15. 15.In which quadrant does the point (−4, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
16. 16.What is the midpoint of the line joining (6, 17) and (12, 7)? (a) (9, 12) (b) (12, 9) (c) (3, 5) (d) (18, 24)
17. 17.In which quadrant does the point (−8, 5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
18. 18.What is the midpoint of the line joining (2, 10) and (14, 2)? (a) (16, 12) (b) (6, 8) (c) (6, 4) (d) (8, 6)
19. 19.In which quadrant does the point (−5, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
20. 20.In which quadrant does the point (−8, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
21. 21.What is the distance between the points (0, 5) and (7, 29)? (a) 625 (b) 25 (c) 26 (d) 31
22. 22.In which quadrant does the point (−7, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
23. 23.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
24. 24.What is the midpoint of the line joining (6, 12) and (16, 2)? (a) (7, 11) (b) (5, 5) (c) (22, 14) (d) (11, 7)
25. 25.What is the distance between the points (7, 13) and (13, 5)? (a) 11 (b) 10 (c) 14 (d) 100
26. 26.What is the distance between the points (6, 5) and (18, 14)? (a) 225 (b) 15 (c) 16 (d) 21
27. 27.What is the distance between the points (1, 13) and (4, 9)? (a) 7 (b) 5 (c) 6 (d) 25
28. 28.In which quadrant does the point (4, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
29. 29.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
30. 30.What is the distance between the points (1, 9) and (9, 15)? (a) 14 (b) 11 (c) 100 (d) 10
31. 31.What is the distance between the points (2, 7) and (14, 16)? (a) 16 (b) 15 (c) 225 (d) 21
32. 32.In which quadrant does the point (4, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
33. 33.In which quadrant does the point (−2, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
34. 34.In which quadrant does the point (1, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
35. 35.What is the distance between the points (8, 9) and (32, 2)? (a) 31 (b) 625 (c) 26 (d) 25
36. 36.What is the midpoint of the line joining (8, 9) and (18, 19)? (a) (13, 14) (b) (5, 5) (c) (14, 13) (d) (26, 28)
37. 37.What is the midpoint of the line joining (0, 20) and (8, 8)? (a) (8, 28) (b) (14, 4) (c) (4, 6) (d) (4, 14)
38. 38.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
39. 39.In which quadrant does the point (6, 4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
40. 40.What is the midpoint of the line joining (3, 2) and (15, 10)? (a) (6, 4) (b) (18, 12) (c) (9, 6) (d) (6, 9)

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