Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 50 · 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 (1, 19) and (9, 4)? (a) 18 (b) 289 (c) 23 (d) 17
2. 2.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
3. 3.What is the midpoint of the line joining (1, 8) and (7, 12)? (a) (10, 4) (b) (4, 10) (c) (3, 2) (d) (8, 20)
4. 4.What is the midpoint of the line joining (5, 18) and (11, 6)? (a) (16, 24) (b) (12, 8) (c) (3, 6) (d) (8, 12)
5. 5.In which quadrant does the point (5, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
6. 6.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
7. 7.What is the midpoint of the line joining (3, 3) and (13, 7)? (a) (8, 5) (b) (5, 2) (c) (16, 10) (d) (5, 8)
8. 8.What is the midpoint of the line joining (7, 7) and (13, 9)? (a) (20, 16) (b) (10, 8) (c) (3, 1) (d) (8, 10)
9. 9.What is the distance between the points (5, 14) and (21, 2)? (a) 400 (b) 28 (c) 20 (d) 21
10. 10.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
11. 11.What is the midpoint of the line joining (7, 8) and (17, 2)? (a) (5, 12) (b) (12, 5) (c) (5, 3) (d) (24, 10)
12. 12.In which quadrant does the point (4, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
13. 13.In which quadrant does the point (3, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
14. 14.What is the midpoint of the line joining (3, 4) and (7, 2)? (a) (10, 6) (b) (2, 1) (c) (5, 3) (d) (3, 5)
15. 15.In which quadrant does the point (1, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
16. 16.In which quadrant does the point (8, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
17. 17.What is the midpoint of the line joining (5, 6) and (15, 0)? (a) (5, 3) (b) (10, 3) (c) (20, 6) (d) (3, 10)
18. 18.What is the distance between the points (1, 1) and (4, 5)? (a) 7 (b) 5 (c) 6 (d) 25
19. 19.What is the midpoint of the line joining (2, 4) and (4, 8)? (a) (3, 6) (b) (1, 2) (c) (6, 12) (d) (6, 3)
20. 20.What is the midpoint of the line joining (7, 9) and (19, 11)? (a) (6, 1) (b) (10, 13) (c) (26, 20) (d) (13, 10)
21. 21.What is the distance between the points (5, 6) and (13, 21)? (a) 289 (b) 18 (c) 23 (d) 17
22. 22.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
23. 23.In which quadrant does the point (−1, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
24. 24.What is the midpoint of the line joining (5, 16) and (7, 8)? (a) (12, 24) (b) (6, 12) (c) (12, 6) (d) (1, 4)
25. 25.What is the distance between the points (1, 8) and (16, 16)? (a) 18 (b) 289 (c) 17 (d) 23
26. 26.What is the midpoint of the line joining (5, 6) and (9, 12)? (a) (2, 3) (b) (9, 7) (c) (14, 18) (d) (7, 9)
27. 27.In which quadrant does the point (8, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
28. 28.What is the midpoint of the line joining (4, 12) and (14, 8)? (a) (18, 20) (b) (9, 10) (c) (5, 2) (d) (10, 9)
29. 29.What is the distance between the points (5, 2) and (21, 14)? (a) 21 (b) 28 (c) 400 (d) 20
30. 30.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
31. 31.In which quadrant does the point (−1, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
32. 32.What is the midpoint of the line joining (7, 9) and (17, 5)? (a) (24, 14) (b) (12, 7) (c) (5, 2) (d) (7, 12)
33. 33.In which quadrant does the point (−5, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
34. 34.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
35. 35.What is the midpoint of the line joining (0, 12) and (12, 8)? (a) (10, 6) (b) (6, 2) (c) (6, 10) (d) (12, 20)
36. 36.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
37. 37.What is the midpoint of the line joining (9, 4) and (19, 2)? (a) (14, 3) (b) (3, 14) (c) (28, 6) (d) (5, 1)
38. 38.What is the midpoint of the line joining (9, 9) and (21, 17)? (a) (15, 13) (b) (30, 26) (c) (6, 4) (d) (13, 15)
39. 39.In which quadrant does the point (−1, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
40. 40.What is the midpoint of the line joining (8, 1) and (18, 5)? (a) (3, 13) (b) (13, 3) (c) (26, 6) (d) (5, 2)

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