Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 99 · 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 (3, 16) and (7, 6)? (a) (5, 11) (b) (10, 22) (c) (11, 5) (d) (2, 5)
2. 2.In which quadrant does the point (2, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
3. 3.In which quadrant does the point (2, 4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
4. 4.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
5. 5.What is the distance between the points (0, 4) and (3, 0)? (a) 7 (b) 25 (c) 5 (d) 6
6. 6.What is the distance between the points (3, 6) and (6, 2)? (a) 6 (b) 7 (c) 5 (d) 25
7. 7.What is the distance between the points (9, 16) and (21, 7)? (a) 225 (b) 15 (c) 16 (d) 21
8. 8.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
9. 9.What is the midpoint of the line joining (0, 5) and (6, 11)? (a) (3, 8) (b) (3, 3) (c) (8, 3) (d) (6, 16)
10. 10.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
11. 11.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
12. 12.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
13. 13.What is the distance between the points (4, 6) and (28, 13)? (a) 625 (b) 31 (c) 25 (d) 26
14. 14.In which quadrant does the point (−6, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
15. 15.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
16. 16.What is the midpoint of the line joining (3, 5) and (5, 17)? (a) (8, 22) (b) (4, 11) (c) (1, 6) (d) (11, 4)
17. 17.In which quadrant does the point (2, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
18. 18.What is the distance between the points (9, 9) and (15, 17)? (a) 100 (b) 10 (c) 11 (d) 14
19. 19.What is the midpoint of the line joining (2, 15) and (14, 9)? (a) (6, 3) (b) (12, 8) (c) (16, 24) (d) (8, 12)
20. 20.What is the distance between the points (7, 17) and (23, 5)? (a) 21 (b) 400 (c) 28 (d) 20
21. 21.What is the midpoint of the line joining (5, 9) and (13, 13)? (a) (9, 11) (b) (11, 9) (c) (18, 22) (d) (4, 2)
22. 22.In which quadrant does the point (−9, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
23. 23.What is the midpoint of the line joining (6, 16) and (16, 8)? (a) (5, 4) (b) (11, 12) (c) (12, 11) (d) (22, 24)
24. 24.What is the distance between the points (0, 4) and (7, 28)? (a) 26 (b) 25 (c) 31 (d) 625
25. 25.What is the midpoint of the line joining (2, 16) and (10, 8)? (a) (12, 24) (b) (6, 12) (c) (4, 4) (d) (12, 6)
26. 26.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
27. 27.In which quadrant does the point (−3, −7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
28. 28.In which quadrant does the point (4, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
29. 29.What is the distance between the points (0, 0) and (9, 12)? (a) 16 (b) 225 (c) 21 (d) 15
30. 30.What is the distance between the points (3, 4) and (15, 13)? (a) 16 (b) 21 (c) 225 (d) 15
31. 31.What is the distance between the points (1, 4) and (5, 1)? (a) 25 (b) 7 (c) 6 (d) 5
32. 32.What is the distance between the points (2, 5) and (18, 17)? (a) 21 (b) 20 (c) 400 (d) 28
33. 33.What is the midpoint of the line joining (6, 0) and (10, 6)? (a) (2, 3) (b) (3, 8) (c) (16, 6) (d) (8, 3)
34. 34.What is the midpoint of the line joining (2, 12) and (8, 6)? (a) (3, 3) (b) (10, 18) (c) (5, 9) (d) (9, 5)
35. 35.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
36. 36.What is the midpoint of the line joining (10, 3) and (14, 1)? (a) (2, 1) (b) (12, 2) (c) (2, 12) (d) (24, 4)
37. 37.What is the distance between the points (9, 10) and (21, 1)? (a) 21 (b) 16 (c) 225 (d) 15
38. 38.What is the midpoint of the line joining (3, 0) and (5, 12)? (a) (6, 4) (b) (1, 6) (c) (4, 6) (d) (8, 12)
39. 39.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
40. 40.In which quadrant does the point (8, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant

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