Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 685 · 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.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
2. 2.What is the midpoint of the line joining (6, 9) and (16, 5)? (a) (7, 11) (b) (5, 2) (c) (22, 14) (d) (11, 7)
3. 3.What is the distance between the points (6, 5) and (21, 13)? (a) 18 (b) 289 (c) 17 (d) 23
4. 4.What is the distance between the points (8, 2) and (24, 14)? (a) 21 (b) 400 (c) 28 (d) 20
5. 5.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
6. 6.What is the midpoint of the line joining (3, 4) and (7, 10)? (a) (10, 14) (b) (7, 5) (c) (2, 3) (d) (5, 7)
7. 7.What is the distance between the points (1, 15) and (16, 7)? (a) 289 (b) 23 (c) 18 (d) 17
8. 8.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
9. 9.What is the midpoint of the line joining (5, 8) and (17, 2)? (a) (6, 3) (b) (11, 5) (c) (5, 11) (d) (22, 10)
10. 10.What is the distance between the points (5, 10) and (29, 3)? (a) 625 (b) 25 (c) 26 (d) 31
11. 11.What is the distance between the points (3, 8) and (15, 17)? (a) 16 (b) 15 (c) 225 (d) 21
12. 12.What is the distance between the points (8, 11) and (12, 8)? (a) 7 (b) 5 (c) 6 (d) 25
13. 13.What is the midpoint of the line joining (1, 18) and (7, 8)? (a) (3, 5) (b) (8, 26) (c) (13, 4) (d) (4, 13)
14. 14.What is the midpoint of the line joining (0, 10) and (6, 22)? (a) (6, 32) (b) (3, 16) (c) (16, 3) (d) (3, 6)
15. 15.What is the midpoint of the line joining (9, 0) and (19, 4)? (a) (28, 4) (b) (2, 14) (c) (14, 2) (d) (5, 2)
16. 16.What is the distance between the points (0, 4) and (4, 7)? (a) 25 (b) 6 (c) 5 (d) 7
17. 17.What is the distance between the points (2, 11) and (14, 6)? (a) 169 (b) 13 (c) 17 (d) 14
18. 18.What is the midpoint of the line joining (7, 6) and (15, 0)? (a) (3, 11) (b) (11, 3) (c) (22, 6) (d) (4, 3)
19. 19.What is the midpoint of the line joining (7, 12) and (9, 10)? (a) (1, 1) (b) (8, 11) (c) (16, 22) (d) (11, 8)
20. 20.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
21. 21.What is the midpoint of the line joining (7, 4) and (11, 14)? (a) (9, 9) (b) (2, 5) (c) (10, 9) (d) (18, 18)
22. 22.What is the distance between the points (5, 17) and (13, 2)? (a) 18 (b) 17 (c) 289 (d) 23
23. 23.In which quadrant does the point (−8, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
24. 24.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
25. 25.What is the midpoint of the line joining (7, 3) and (17, 1)? (a) (2, 12) (b) (24, 4) (c) (12, 2) (d) (5, 1)
26. 26.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
27. 27.What is the midpoint of the line joining (0, 14) and (2, 10)? (a) (1, 12) (b) (2, 24) (c) (1, 2) (d) (12, 1)
28. 28.What is the midpoint of the line joining (9, 3) and (21, 7)? (a) (6, 2) (b) (30, 10) (c) (15, 5) (d) (5, 15)
29. 29.In which quadrant does the point (−6, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
30. 30.What is the distance between the points (2, 8) and (26, 1)? (a) 26 (b) 31 (c) 25 (d) 625
31. 31.What is the midpoint of the line joining (5, 6) and (17, 10)? (a) (8, 11) (b) (6, 2) (c) (22, 16) (d) (11, 8)
32. 32.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
33. 33.What is the distance between the points (8, 4) and (11, 0)? (a) 25 (b) 5 (c) 6 (d) 7
34. 34.What is the midpoint of the line joining (9, 1) and (13, 5)? (a) (3, 11) (b) (11, 3) (c) (2, 2) (d) (22, 6)
35. 35.What is the distance between the points (2, 7) and (18, 19)? (a) 21 (b) 28 (c) 400 (d) 20
36. 36.What is the distance between the points (3, 16) and (18, 8)? (a) 17 (b) 23 (c) 18 (d) 289
37. 37.What is the midpoint of the line joining (8, 8) and (18, 14)? (a) (5, 3) (b) (11, 13) (c) (13, 11) (d) (26, 22)
38. 38.What is the midpoint of the line joining (9, 8) and (11, 18)? (a) (13, 10) (b) (20, 26) (c) (10, 13) (d) (1, 5)
39. 39.What is the distance between the points (3, 21) and (15, 5)? (a) 21 (b) 400 (c) 20 (d) 28
40. 40.What is the midpoint of the line joining (2, 20) and (4, 10)? (a) (1, 5) (b) (3, 15) (c) (15, 3) (d) (6, 30)

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