Coordinate Geometry Worksheet for Maths Olympiad

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

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