Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 65 · 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 (1, 18) and (13, 9)? (a) 15 (b) 16 (c) 21 (d) 225
2. 2.What is the midpoint of the line joining (1, 9) and (11, 13)? (a) (11, 6) (b) (5, 2) (c) (6, 11) (d) (12, 22)
3. 3.What is the distance between the points (1, 2) and (9, 17)? (a) 23 (b) 289 (c) 18 (d) 17
4. 4.What is the midpoint of the line joining (9, 11) and (17, 3)? (a) (4, 4) (b) (7, 13) (c) (26, 14) (d) (13, 7)
5. 5.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
6. 6.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
7. 7.What is the distance between the points (0, 3) and (9, 15)? (a) 225 (b) 21 (c) 16 (d) 15
8. 8.What is the midpoint of the line joining (5, 7) and (11, 3)? (a) (3, 2) (b) (8, 5) (c) (5, 8) (d) (16, 10)
9. 9.What is the midpoint of the line joining (1, 7) and (5, 3)? (a) (2, 2) (b) (3, 5) (c) (5, 3) (d) (6, 10)
10. 10.In which quadrant does the point (−7, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
11. 11.What is the distance between the points (0, 14) and (5, 2)? (a) 13 (b) 17 (c) 169 (d) 14
12. 12.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
13. 13.In which quadrant does the point (−9, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
14. 14.What is the distance between the points (1, 0) and (4, 4)? (a) 25 (b) 7 (c) 6 (d) 5
15. 15.What is the midpoint of the line joining (7, 8) and (17, 12)? (a) (12, 10) (b) (5, 2) (c) (24, 20) (d) (10, 12)
16. 16.What is the distance between the points (2, 8) and (10, 23)? (a) 17 (b) 18 (c) 23 (d) 289
17. 17.What is the midpoint of the line joining (0, 1) and (6, 13)? (a) (3, 7) (b) (3, 6) (c) (6, 14) (d) (7, 3)
18. 18.What is the distance between the points (5, 16) and (13, 1)? (a) 23 (b) 289 (c) 17 (d) 18
19. 19.What is the midpoint of the line joining (2, 10) and (4, 18)? (a) (3, 14) (b) (6, 28) (c) (1, 4) (d) (14, 3)
20. 20.What is the midpoint of the line joining (1, 20) and (11, 10)? (a) (15, 6) (b) (5, 5) (c) (12, 30) (d) (6, 15)
21. 21.What is the distance between the points (3, 2) and (19, 14)? (a) 400 (b) 20 (c) 21 (d) 28
22. 22.What is the distance between the points (2, 15) and (17, 7)? (a) 23 (b) 289 (c) 18 (d) 17
23. 23.What is the midpoint of the line joining (0, 2) and (12, 8)? (a) (5, 6) (b) (6, 3) (c) (6, 5) (d) (12, 10)
24. 24.What is the distance between the points (5, 7) and (14, 19)? (a) 21 (b) 225 (c) 15 (d) 16
25. 25.What is the distance between the points (9, 3) and (12, 7)? (a) 7 (b) 6 (c) 5 (d) 25
26. 26.What is the distance between the points (1, 22) and (13, 6)? (a) 400 (b) 20 (c) 28 (d) 21
27. 27.What is the distance between the points (4, 2) and (10, 10)? (a) 14 (b) 10 (c) 11 (d) 100
28. 28.What is the midpoint of the line joining (2, 11) and (10, 7)? (a) (6, 9) (b) (12, 18) (c) (4, 2) (d) (9, 6)
29. 29.What is the midpoint of the line joining (2, 8) and (12, 10)? (a) (7, 9) (b) (9, 7) (c) (5, 1) (d) (14, 18)
30. 30.What is the distance between the points (0, 21) and (8, 6)? (a) 23 (b) 18 (c) 17 (d) 289
31. 31.What is the midpoint of the line joining (3, 6) and (13, 2)? (a) (5, 2) (b) (16, 8) (c) (4, 8) (d) (8, 4)
32. 32.What is the midpoint of the line joining (2, 4) and (8, 10)? (a) (3, 3) (b) (10, 14) (c) (5, 7) (d) (7, 5)
33. 33.What is the midpoint of the line joining (9, 12) and (21, 10)? (a) (11, 15) (b) (6, 1) (c) (30, 22) (d) (15, 11)
34. 34.In which quadrant does the point (−6, −9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
35. 35.What is the midpoint of the line joining (2, 10) and (14, 0)? (a) (6, 5) (b) (16, 10) (c) (8, 5) (d) (5, 8)
36. 36.What is the distance between the points (4, 6) and (7, 10)? (a) 6 (b) 7 (c) 25 (d) 5
37. 37.What is the distance between the points (8, 19) and (20, 3)? (a) 20 (b) 21 (c) 400 (d) 28
38. 38.What is the midpoint of the line joining (6, 13) and (16, 7)? (a) (22, 20) (b) (11, 10) (c) (5, 3) (d) (10, 11)
39. 39.What is the distance between the points (9, 1) and (14, 13)? (a) 13 (b) 14 (c) 169 (d) 17
40. 40.What is the midpoint of the line joining (6, 11) and (8, 1)? (a) (7, 6) (b) (1, 5) (c) (14, 12) (d) (6, 7)

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