Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 409 · 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 (0, 3) and (15, 11)? (a) 18 (b) 23 (c) 17 (d) 289
2. 2.What is the distance between the points (3, 2) and (27, 9)? (a) 26 (b) 31 (c) 625 (d) 25
3. 3.What is the midpoint of the line joining (0, 9) and (10, 1)? (a) (6, 5) (b) (5, 4) (c) (10, 10) (d) (5, 5)
4. 4.In which quadrant does the point (−4, 9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
5. 5.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
6. 6.What is the distance between the points (0, 12) and (9, 0)? (a) 225 (b) 15 (c) 16 (d) 21
7. 7.What is the midpoint of the line joining (4, 6) and (8, 0)? (a) (12, 6) (b) (2, 3) (c) (6, 3) (d) (3, 6)
8. 8.What is the distance between the points (1, 2) and (6, 14)? (a) 14 (b) 13 (c) 169 (d) 17
9. 9.In which quadrant does the point (−7, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
10. 10.What is the distance between the points (1, 6) and (13, 1)? (a) 14 (b) 13 (c) 17 (d) 169
11. 11.What is the distance between the points (4, 14) and (9, 2)? (a) 17 (b) 169 (c) 13 (d) 14
12. 12.In which quadrant does the point (4, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
13. 13.What is the midpoint of the line joining (5, 0) and (15, 6)? (a) (5, 3) (b) (20, 6) (c) (3, 10) (d) (10, 3)
14. 14.In which quadrant does the point (8, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
15. 15.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
16. 16.What is the distance between the points (8, 6) and (12, 9)? (a) 25 (b) 5 (c) 6 (d) 7
17. 17.What is the midpoint of the line joining (4, 19) and (8, 9)? (a) (6, 14) (b) (2, 5) (c) (14, 6) (d) (12, 28)
18. 18.What is the distance between the points (9, 1) and (15, 9)? (a) 100 (b) 14 (c) 10 (d) 11
19. 19.What is the distance between the points (9, 3) and (12, 7)? (a) 6 (b) 7 (c) 25 (d) 5
20. 20.What is the distance between the points (9, 13) and (25, 1)? (a) 21 (b) 28 (c) 400 (d) 20
21. 21.What is the distance between the points (1, 15) and (25, 8)? (a) 25 (b) 625 (c) 26 (d) 31
22. 22.What is the distance between the points (1, 6) and (13, 15)? (a) 16 (b) 225 (c) 21 (d) 15
23. 23.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
24. 24.In which quadrant does the point (−1, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
26. 26.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
27. 27.In which quadrant does the point (2, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
28. 28.What is the distance between the points (0, 2) and (12, 18)? (a) 21 (b) 20 (c) 28 (d) 400
29. 29.In which quadrant does the point (6, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
30. 30.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
31. 31.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
32. 32.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
33. 33.What is the distance between the points (2, 31) and (9, 7)? (a) 625 (b) 26 (c) 31 (d) 25
34. 34.In which quadrant does the point (−9, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
35. 35.What is the midpoint of the line joining (0, 4) and (2, 14)? (a) (2, 18) (b) (1, 9) (c) (9, 1) (d) (1, 5)
36. 36.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
37. 37.In which quadrant does the point (−8, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
38. 38.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
39. 39.What is the distance between the points (3, 18) and (15, 9)? (a) 21 (b) 15 (c) 225 (d) 16
40. 40.What is the midpoint of the line joining (5, 15) and (7, 3)? (a) (9, 6) (b) (12, 18) (c) (1, 6) (d) (6, 9)

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