Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 568 · 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) 400 (b) 28 (c) 20 (d) 21
2. 2.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
3. 3.What is the distance between the points (2, 33) and (9, 9)? (a) 625 (b) 25 (c) 26 (d) 31
4. 4.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
5. 5.What is the distance between the points (8, 3) and (32, 10)? (a) 25 (b) 31 (c) 26 (d) 625
6. 6.In which quadrant does the point (7, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
7. 7.What is the midpoint of the line joining (0, 8) and (10, 12)? (a) (10, 20) (b) (5, 2) (c) (5, 10) (d) (10, 5)
8. 8.What is the midpoint of the line joining (9, 18) and (13, 6)? (a) (2, 6) (b) (11, 12) (c) (22, 24) (d) (12, 11)
9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
10. 10.What is the midpoint of the line joining (0, 2) and (4, 10)? (a) (6, 2) (b) (4, 12) (c) (2, 4) (d) (2, 6)
11. 11.What is the midpoint of the line joining (1, 15) and (9, 3)? (a) (4, 6) (b) (9, 5) (c) (10, 18) (d) (5, 9)
12. 12.What is the distance between the points (2, 2) and (14, 11)? (a) 15 (b) 16 (c) 21 (d) 225
13. 13.What is the distance between the points (1, 9) and (10, 21)? (a) 15 (b) 16 (c) 225 (d) 21
14. 14.What is the midpoint of the line joining (10, 15) and (16, 9)? (a) (26, 24) (b) (12, 13) (c) (13, 12) (d) (3, 3)
15. 15.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
16. 16.In which quadrant does the point (6, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
17. 17.In which quadrant does the point (5, −9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
18. 18.What is the midpoint of the line joining (5, 18) and (11, 6)? (a) (12, 8) (b) (3, 6) (c) (16, 24) (d) (8, 12)
19. 19.In which quadrant does the point (−4, −6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
20. 20.In which quadrant does the point (−1, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
21. 21.What is the midpoint of the line joining (4, 0) and (8, 2)? (a) (12, 2) (b) (6, 1) (c) (1, 6) (d) (2, 1)
22. 22.What is the midpoint of the line joining (2, 1) and (12, 5)? (a) (7, 3) (b) (14, 6) (c) (5, 2) (d) (3, 7)
23. 23.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
24. 24.What is the distance between the points (6, 21) and (15, 9)? (a) 16 (b) 225 (c) 21 (d) 15
25. 25.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
26. 26.What is the midpoint of the line joining (5, 6) and (7, 18)? (a) (1, 6) (b) (12, 24) (c) (6, 12) (d) (12, 6)
27. 27.What is the distance between the points (4, 17) and (9, 5)? (a) 14 (b) 169 (c) 13 (d) 17
28. 28.In which quadrant does the point (2, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
29. 29.What is the distance between the points (2, 3) and (6, 6)? (a) 7 (b) 5 (c) 25 (d) 6
30. 30.What is the distance between the points (4, 7) and (12, 1)? (a) 100 (b) 11 (c) 14 (d) 10
31. 31.What is the midpoint of the line joining (10, 14) and (14, 10)? (a) (24, 24) (b) (13, 12) (c) (2, 2) (d) (12, 12)
32. 32.What is the distance between the points (2, 6) and (17, 14)? (a) 17 (b) 289 (c) 18 (d) 23
33. 33.In which quadrant does the point (4, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
34. 34.What is the distance between the points (4, 33) and (11, 9)? (a) 625 (b) 31 (c) 26 (d) 25
35. 35.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
36. 36.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
37. 37.What is the midpoint of the line joining (8, 5) and (14, 15)? (a) (3, 5) (b) (10, 11) (c) (11, 10) (d) (22, 20)
38. 38.What is the distance between the points (0, 2) and (15, 10)? (a) 289 (b) 17 (c) 18 (d) 23
39. 39.What is the distance between the points (7, 5) and (19, 10)? (a) 14 (b) 13 (c) 169 (d) 17
40. 40.What is the midpoint of the line joining (1, 1) and (7, 13)? (a) (3, 6) (b) (8, 14) (c) (7, 4) (d) (4, 7)

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