Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 687 · 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) 289 (b) 23 (c) 18 (d) 17
2. 2.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
3. 3.What is the distance between the points (3, 7) and (12, 19)? (a) 15 (b) 225 (c) 21 (d) 16
4. 4.In which quadrant does the point (−7, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
5. 5.What is the distance between the points (3, 16) and (8, 4)? (a) 17 (b) 14 (c) 13 (d) 169
6. 6.What is the distance between the points (8, 9) and (20, 25)? (a) 400 (b) 21 (c) 28 (d) 20
7. 7.What is the midpoint of the line joining (9, 6) and (11, 0)? (a) (3, 10) (b) (20, 6) (c) (10, 3) (d) (1, 3)
8. 8.What is the midpoint of the line joining (7, 4) and (13, 6)? (a) (5, 10) (b) (10, 5) (c) (3, 1) (d) (20, 10)
9. 9.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
10. 10.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
11. 11.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
12. 12.What is the distance between the points (5, 8) and (29, 1)? (a) 625 (b) 26 (c) 25 (d) 31
13. 13.What is the distance between the points (7, 20) and (15, 5)? (a) 289 (b) 18 (c) 17 (d) 23
14. 14.What is the distance between the points (9, 7) and (21, 16)? (a) 21 (b) 225 (c) 15 (d) 16
15. 15.What is the midpoint of the line joining (7, 2) and (11, 8)? (a) (2, 3) (b) (9, 5) (c) (18, 10) (d) (5, 9)
16. 16.What is the midpoint of the line joining (1, 9) and (5, 15)? (a) (6, 24) (b) (3, 12) (c) (2, 3) (d) (12, 3)
17. 17.In which quadrant does the point (−3, 9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
18. 18.What is the midpoint of the line joining (9, 6) and (19, 0)? (a) (28, 6) (b) (5, 3) (c) (3, 14) (d) (14, 3)
19. 19.What is the distance between the points (6, 6) and (18, 11)? (a) 169 (b) 17 (c) 14 (d) 13
20. 20.In which quadrant does the point (4, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
21. 21.In which quadrant does the point (9, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
22. 22.In which quadrant does the point (8, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
23. 23.What is the midpoint of the line joining (3, 7) and (7, 13)? (a) (10, 5) (b) (10, 20) (c) (2, 3) (d) (5, 10)
24. 24.In which quadrant does the point (−6, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
25. 25.What is the midpoint of the line joining (10, 5) and (14, 9)? (a) (12, 7) (b) (7, 12) (c) (2, 2) (d) (24, 14)
26. 26.What is the distance between the points (1, 9) and (4, 5)? (a) 25 (b) 6 (c) 5 (d) 7
27. 27.What is the distance between the points (0, 3) and (16, 15)? (a) 20 (b) 21 (c) 400 (d) 28
28. 28.In which quadrant does the point (9, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
29. 29.What is the midpoint of the line joining (3, 5) and (7, 9)? (a) (5, 7) (b) (10, 14) (c) (2, 2) (d) (7, 5)
30. 30.What is the midpoint of the line joining (8, 2) and (12, 0)? (a) (2, 1) (b) (10, 1) (c) (20, 2) (d) (1, 10)
31. 31.What is the distance between the points (2, 8) and (9, 32)? (a) 625 (b) 31 (c) 25 (d) 26
32. 32.What is the distance between the points (6, 13) and (18, 4)? (a) 15 (b) 16 (c) 225 (d) 21
33. 33.What is the midpoint of the line joining (6, 6) and (16, 10)? (a) (5, 2) (b) (8, 11) (c) (22, 16) (d) (11, 8)
34. 34.What is the midpoint of the line joining (10, 8) and (16, 12)? (a) (10, 13) (b) (26, 20) (c) (3, 2) (d) (13, 10)
35. 35.What is the distance between the points (3, 1) and (15, 6)? (a) 169 (b) 14 (c) 17 (d) 13
36. 36.What is the midpoint of the line joining (1, 14) and (9, 4)? (a) (10, 18) (b) (4, 5) (c) (5, 9) (d) (9, 5)
37. 37.What is the midpoint of the line joining (3, 4) and (9, 14)? (a) (9, 6) (b) (12, 18) (c) (3, 5) (d) (6, 9)
38. 38.What is the midpoint of the line joining (10, 9) and (16, 17)? (a) (26, 26) (b) (3, 4) (c) (14, 13) (d) (13, 13)
39. 39.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
40. 40.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625

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