Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 97 · 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 (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
2. 2.What is the distance between the points (9, 7) and (12, 11)? (a) 5 (b) 25 (c) 6 (d) 7
3. 3.What is the midpoint of the line joining (8, 3) and (10, 5)? (a) (9, 4) (b) (1, 1) (c) (18, 8) (d) (4, 9)
4. 4.In which quadrant does the point (−8, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
5. 5.What is the distance between the points (1, 6) and (9, 12)? (a) 100 (b) 11 (c) 14 (d) 10
6. 6.In which quadrant does the point (−7, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
7. 7.What is the distance between the points (0, 7) and (8, 13)? (a) 100 (b) 11 (c) 14 (d) 10
8. 8.What is the midpoint of the line joining (0, 16) and (6, 4)? (a) (3, 10) (b) (10, 3) (c) (6, 20) (d) (3, 6)
9. 9.In which quadrant does the point (5, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
10. 10.In which quadrant does the point (−4, −7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
11. 11.In which quadrant does the point (−4, −9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
12. 12.What is the midpoint of the line joining (10, 3) and (22, 1)? (a) (16, 2) (b) (6, 1) (c) (2, 16) (d) (32, 4)
13. 13.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
14. 14.In which quadrant does the point (−9, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
15. 15.What is the midpoint of the line joining (5, 8) and (11, 12)? (a) (3, 2) (b) (16, 20) (c) (10, 8) (d) (8, 10)
16. 16.In which quadrant does the point (2, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
17. 17.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
18. 18.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
19. 19.What is the midpoint of the line joining (9, 0) and (19, 10)? (a) (14, 5) (b) (5, 5) (c) (5, 14) (d) (28, 10)
20. 20.What is the distance between the points (5, 20) and (21, 8)? (a) 20 (b) 400 (c) 21 (d) 28
21. 21.In which quadrant does the point (1, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
22. 22.What is the distance between the points (5, 20) and (14, 8)? (a) 16 (b) 225 (c) 21 (d) 15
23. 23.What is the midpoint of the line joining (4, 9) and (12, 19)? (a) (16, 28) (b) (14, 8) (c) (4, 5) (d) (8, 14)
24. 24.In which quadrant does the point (3, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
25. 25.In which quadrant does the point (−8, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
26. 26.What is the distance between the points (0, 23) and (8, 8)? (a) 289 (b) 17 (c) 18 (d) 23
27. 27.What is the midpoint of the line joining (1, 7) and (3, 17)? (a) (1, 5) (b) (2, 12) (c) (12, 2) (d) (4, 24)
28. 28.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
29. 29.In which quadrant does the point (−2, 2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
30. 30.In which quadrant does the point (−6, 5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
31. 31.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
32. 32.In which quadrant does the point (3, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
33. 33.What is the distance between the points (4, 1) and (11, 25)? (a) 31 (b) 26 (c) 25 (d) 625
34. 34.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
35. 35.In which quadrant does the point (−8, −5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
36. 36.In which quadrant does the point (4, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
37. 37.What is the midpoint of the line joining (7, 8) and (15, 16)? (a) (22, 24) (b) (4, 4) (c) (11, 12) (d) (12, 11)
38. 38.In which quadrant does the point (2, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
39. 39.What is the distance between the points (8, 8) and (14, 16)? (a) 100 (b) 11 (c) 10 (d) 14
40. 40.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5

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