Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 323 · 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, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
2. 2.What is the midpoint of the line joining (0, 12) and (4, 6)? (a) (2, 9) (b) (4, 18) (c) (9, 2) (d) (2, 3)
3. 3.What is the distance between the points (9, 4) and (21, 9)? (a) 17 (b) 14 (c) 13 (d) 169
4. 4.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
5. 5.What is the midpoint of the line joining (1, 10) and (5, 0)? (a) (5, 3) (b) (3, 5) (c) (2, 5) (d) (6, 10)
6. 6.What is the distance between the points (0, 0) and (8, 15)? (a) 289 (b) 23 (c) 18 (d) 17
7. 7.In which quadrant does the point (9, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
8. 8.What is the midpoint of the line joining (2, 8) and (6, 14)? (a) (4, 11) (b) (2, 3) (c) (8, 22) (d) (11, 4)
9. 9.What is the midpoint of the line joining (0, 6) and (6, 2)? (a) (4, 3) (b) (3, 4) (c) (6, 8) (d) (3, 2)
10. 10.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
11. 11.What is the distance between the points (1, 5) and (6, 17)? (a) 169 (b) 13 (c) 17 (d) 14
12. 12.What is the distance between the points (7, 6) and (10, 2)? (a) 7 (b) 25 (c) 6 (d) 5
13. 13.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
14. 14.What is the midpoint of the line joining (7, 10) and (17, 0)? (a) (5, 12) (b) (24, 10) (c) (12, 5) (d) (5, 5)
15. 15.What is the midpoint of the line joining (7, 0) and (19, 4)? (a) (13, 2) (b) (6, 2) (c) (26, 4) (d) (2, 13)
16. 16.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
17. 17.What is the midpoint of the line joining (1, 0) and (5, 6)? (a) (4, 3) (b) (6, 6) (c) (3, 3) (d) (2, 3)
18. 18.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
19. 19.What is the midpoint of the line joining (7, 2) and (9, 0)? (a) (1, 8) (b) (1, 1) (c) (16, 2) (d) (8, 1)
20. 20.In which quadrant does the point (−2, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
21. 21.What is the midpoint of the line joining (10, 15) and (18, 7)? (a) (11, 14) (b) (4, 4) (c) (14, 11) (d) (28, 22)
22. 22.What is the distance between the points (0, 9) and (9, 21)? (a) 225 (b) 15 (c) 21 (d) 16
23. 23.What is the midpoint of the line joining (3, 18) and (13, 8)? (a) (13, 8) (b) (16, 26) (c) (5, 5) (d) (8, 13)
24. 24.What is the midpoint of the line joining (9, 0) and (15, 2)? (a) (3, 1) (b) (12, 1) (c) (1, 12) (d) (24, 2)
25. 25.What is the midpoint of the line joining (7, 2) and (17, 4)? (a) (3, 12) (b) (24, 6) (c) (5, 1) (d) (12, 3)
26. 26.What is the midpoint of the line joining (9, 13) and (17, 9)? (a) (26, 22) (b) (4, 2) (c) (13, 11) (d) (11, 13)
27. 27.What is the midpoint of the line joining (9, 7) and (15, 17)? (a) (13, 12) (b) (24, 24) (c) (12, 12) (d) (3, 5)
28. 28.What is the midpoint of the line joining (1, 19) and (13, 9)? (a) (14, 28) (b) (14, 7) (c) (7, 14) (d) (6, 5)
29. 29.What is the midpoint of the line joining (7, 3) and (11, 7)? (a) (18, 10) (b) (5, 9) (c) (9, 5) (d) (2, 2)
30. 30.What is the distance between the points (0, 2) and (12, 18)? (a) 28 (b) 20 (c) 21 (d) 400
31. 31.What is the distance between the points (7, 2) and (19, 7)? (a) 17 (b) 169 (c) 14 (d) 13
32. 32.What is the distance between the points (1, 6) and (9, 12)? (a) 100 (b) 11 (c) 10 (d) 14
33. 33.What is the midpoint of the line joining (0, 0) and (4, 8)? (a) (4, 8) (b) (4, 2) (c) (3, 4) (d) (2, 4)
34. 34.What is the distance between the points (8, 5) and (15, 29)? (a) 26 (b) 625 (c) 31 (d) 25
35. 35.What is the distance between the points (7, 9) and (22, 17)? (a) 23 (b) 289 (c) 18 (d) 17
36. 36.In which quadrant does the point (5, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
37. 37.What is the distance between the points (0, 10) and (24, 3)? (a) 31 (b) 25 (c) 26 (d) 625
38. 38.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
39. 39.In which quadrant does the point (1, 2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
40. 40.What is the distance between the points (8, 3) and (32, 10)? (a) 625 (b) 31 (c) 26 (d) 25

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