Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 42 · 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 distance between the points (2, 8) and (8, 0)? (a) 14 (b) 11 (c) 100 (d) 10
2. 2.What is the midpoint of the line joining (4, 13) and (10, 3)? (a) (8, 7) (b) (3, 5) (c) (7, 8) (d) (14, 16)
3. 3.What is the midpoint of the line joining (0, 7) and (4, 11)? (a) (4, 18) (b) (2, 2) (c) (2, 9) (d) (9, 2)
4. 4.What is the midpoint of the line joining (4, 10) and (10, 18)? (a) (7, 14) (b) (3, 4) (c) (14, 7) (d) (14, 28)
5. 5.What is the distance between the points (1, 6) and (13, 1)? (a) 13 (b) 169 (c) 14 (d) 17
6. 6.What is the distance between the points (3, 13) and (6, 9)? (a) 25 (b) 6 (c) 7 (d) 5
7. 7.What is the distance between the points (8, 5) and (14, 13)? (a) 100 (b) 11 (c) 10 (d) 14
8. 8.What is the distance between the points (6, 4) and (9, 8)? (a) 6 (b) 7 (c) 25 (d) 5
9. 9.What is the midpoint of the line joining (7, 8) and (11, 18)? (a) (13, 9) (b) (18, 26) (c) (2, 5) (d) (9, 13)
10. 10.In which quadrant does the point (4, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
11. 11.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
12. 12.In which quadrant does the point (−8, 7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
13. 13.What is the midpoint of the line joining (0, 4) and (2, 0)? (a) (2, 4) (b) (1, 2) (c) (2, 1) (d) (2, 2)
14. 14.What is the midpoint of the line joining (2, 2) and (10, 10)? (a) (12, 12) (b) (4, 4) (c) (6, 6) (d) (7, 6)
15. 15.What is the midpoint of the line joining (10, 8) and (12, 2)? (a) (5, 11) (b) (11, 5) (c) (22, 10) (d) (1, 3)
16. 16.In which quadrant does the point (9, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
17. 17.What is the distance between the points (6, 6) and (10, 9)? (a) 5 (b) 6 (c) 7 (d) 25
18. 18.In which quadrant does the point (5, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
19. 19.What is the midpoint of the line joining (10, 9) and (20, 19)? (a) (30, 28) (b) (14, 15) (c) (5, 5) (d) (15, 14)
20. 20.What is the distance between the points (9, 21) and (17, 6)? (a) 289 (b) 23 (c) 18 (d) 17
21. 21.What is the midpoint of the line joining (0, 1) and (4, 13)? (a) (7, 2) (b) (4, 14) (c) (2, 6) (d) (2, 7)
22. 22.What is the distance between the points (0, 17) and (16, 5)? (a) 400 (b) 28 (c) 21 (d) 20
23. 23.In which quadrant does the point (−8, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
24. 24.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
25. 25.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
26. 26.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
27. 27.What is the distance between the points (2, 14) and (8, 6)? (a) 11 (b) 100 (c) 14 (d) 10
28. 28.What is the distance between the points (1, 2) and (13, 18)? (a) 28 (b) 21 (c) 20 (d) 400
29. 29.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
30. 30.What is the distance between the points (7, 20) and (15, 5)? (a) 17 (b) 18 (c) 23 (d) 289
31. 31.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
32. 32.In which quadrant does the point (2, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
33. 33.What is the midpoint of the line joining (10, 9) and (16, 7)? (a) (26, 16) (b) (13, 8) (c) (3, 1) (d) (8, 13)
34. 34.What is the midpoint of the line joining (9, 8) and (15, 20)? (a) (14, 12) (b) (3, 6) (c) (12, 14) (d) (24, 28)
35. 35.What is the distance between the points (1, 1) and (13, 17)? (a) 28 (b) 21 (c) 20 (d) 400
36. 36.What is the midpoint of the line joining (1, 10) and (3, 14)? (a) (12, 2) (b) (2, 12) (c) (4, 24) (d) (1, 2)
37. 37.What is the distance between the points (6, 13) and (15, 1)? (a) 225 (b) 21 (c) 16 (d) 15
38. 38.What is the distance between the points (0, 12) and (9, 0)? (a) 225 (b) 16 (c) 21 (d) 15
39. 39.What is the distance between the points (0, 16) and (5, 4)? (a) 14 (b) 17 (c) 13 (d) 169
40. 40.What is the distance between the points (2, 18) and (10, 3)? (a) 17 (b) 289 (c) 23 (d) 18

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