Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 642 · 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 (8, 9) and (16, 19)? (a) (4, 5) (b) (24, 28) (c) (12, 14) (d) (14, 12)
2. 2.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
3. 3.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
4. 4.In which quadrant does the point (2, 9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
5. 5.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
6. 6.What is the distance between the points (2, 16) and (8, 8)? (a) 100 (b) 10 (c) 11 (d) 14
7. 7.What is the distance between the points (1, 5) and (13, 0)? (a) 17 (b) 13 (c) 169 (d) 14
8. 8.What is the distance between the points (5, 0) and (11, 8)? (a) 11 (b) 14 (c) 100 (d) 10
9. 9.What is the midpoint of the line joining (1, 5) and (13, 7)? (a) (6, 7) (b) (14, 12) (c) (6, 1) (d) (7, 6)
10. 10.In which quadrant does the point (−8, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
11. 11.What is the midpoint of the line joining (3, 18) and (9, 10)? (a) (14, 6) (b) (6, 14) (c) (12, 28) (d) (3, 4)
12. 12.In which quadrant does the point (9, −5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
13. 13.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
14. 14.What is the distance between the points (8, 16) and (14, 8)? (a) 14 (b) 100 (c) 10 (d) 11
15. 15.In which quadrant does the point (−9, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
16. 16.What is the midpoint of the line joining (10, 2) and (20, 12)? (a) (7, 15) (b) (5, 5) (c) (30, 14) (d) (15, 7)
17. 17.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
18. 18.In which quadrant does the point (1, 4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
19. 19.What is the midpoint of the line joining (1, 10) and (13, 14)? (a) (14, 24) (b) (6, 2) (c) (7, 12) (d) (12, 7)
20. 20.In which quadrant does the point (−1, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
21. 21.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
22. 22.What is the midpoint of the line joining (1, 10) and (11, 14)? (a) (12, 6) (b) (5, 2) (c) (12, 24) (d) (6, 12)
23. 23.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
24. 24.What is the midpoint of the line joining (9, 11) and (19, 7)? (a) (28, 18) (b) (9, 14) (c) (5, 2) (d) (14, 9)
25. 25.In which quadrant does the point (7, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
26. 26.What is the distance between the points (4, 16) and (9, 4)? (a) 14 (b) 17 (c) 13 (d) 169
27. 27.What is the distance between the points (5, 0) and (21, 12)? (a) 28 (b) 400 (c) 21 (d) 20
28. 28.What is the midpoint of the line joining (10, 9) and (14, 3)? (a) (6, 12) (b) (24, 12) (c) (2, 3) (d) (12, 6)
29. 29.What is the distance between the points (2, 11) and (8, 3)? (a) 11 (b) 100 (c) 10 (d) 14
30. 30.What is the distance between the points (0, 12) and (4, 9)? (a) 25 (b) 5 (c) 6 (d) 7
31. 31.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
32. 32.What is the midpoint of the line joining (6, 17) and (12, 5)? (a) (9, 11) (b) (3, 6) (c) (18, 22) (d) (11, 9)
33. 33.What is the distance between the points (7, 5) and (16, 17)? (a) 16 (b) 21 (c) 225 (d) 15
34. 34.What is the distance between the points (1, 14) and (17, 2)? (a) 21 (b) 28 (c) 20 (d) 400
35. 35.In which quadrant does the point (−3, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
36. 36.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
37. 37.What is the midpoint of the line joining (9, 4) and (13, 16)? (a) (10, 11) (b) (2, 6) (c) (11, 10) (d) (22, 20)
38. 38.What is the midpoint of the line joining (5, 2) and (7, 0)? (a) (6, 1) (b) (1, 1) (c) (1, 6) (d) (12, 2)
39. 39.What is the midpoint of the line joining (9, 16) and (11, 4)? (a) (10, 10) (b) (20, 20) (c) (1, 6) (d) (11, 10)
40. 40.What is the midpoint of the line joining (5, 2) and (15, 10)? (a) (20, 12) (b) (6, 10) (c) (5, 4) (d) (10, 6)

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