Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 839 · 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 midpoint of the line joining (2, 1) and (4, 5)? (a) (3, 3) (b) (4, 3) (c) (1, 2) (d) (6, 6)
2. 2.What is the distance between the points (3, 19) and (11, 4)? (a) 289 (b) 17 (c) 23 (d) 18
3. 3.What is the midpoint of the line joining (0, 11) and (2, 1)? (a) (6, 1) (b) (1, 5) (c) (2, 12) (d) (1, 6)
4. 4.What is the midpoint of the line joining (3, 2) and (9, 10)? (a) (3, 4) (b) (12, 12) (c) (7, 6) (d) (6, 6)
5. 5.What is the midpoint of the line joining (1, 3) and (7, 5)? (a) (5, 4) (b) (8, 8) (c) (4, 4) (d) (3, 1)
6. 6.What is the midpoint of the line joining (9, 14) and (21, 6)? (a) (6, 4) (b) (30, 20) (c) (15, 10) (d) (10, 15)
7. 7.What is the distance between the points (8, 9) and (20, 14)? (a) 169 (b) 14 (c) 13 (d) 17
8. 8.In which quadrant does the point (−9, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
9. 9.In which quadrant does the point (−6, 4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
10. 10.In which quadrant does the point (2, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
12. 12.In which quadrant does the point (2, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
13. 13.In which quadrant does the point (7, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
14. 14.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
15. 15.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
16. 16.What is the midpoint of the line joining (7, 10) and (11, 8)? (a) (18, 18) (b) (10, 9) (c) (2, 1) (d) (9, 9)
17. 17.What is the midpoint of the line joining (10, 5) and (12, 11)? (a) (11, 8) (b) (1, 3) (c) (22, 16) (d) (8, 11)
18. 18.What is the distance between the points (1, 1) and (13, 10)? (a) 21 (b) 15 (c) 225 (d) 16
19. 19.What is the midpoint of the line joining (1, 8) and (5, 10)? (a) (3, 9) (b) (9, 3) (c) (2, 1) (d) (6, 18)
20. 20.In which quadrant does the point (−6, −6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
21. 21.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
22. 22.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
23. 23.In which quadrant does the point (1, 7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
24. 24.What is the midpoint of the line joining (6, 6) and (16, 2)? (a) (11, 4) (b) (22, 8) (c) (4, 11) (d) (5, 2)
25. 25.In which quadrant does the point (8, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
26. 26.In which quadrant does the point (−8, 8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
27. 27.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
28. 28.What is the distance between the points (7, 8) and (31, 1)? (a) 625 (b) 26 (c) 25 (d) 31
29. 29.What is the distance between the points (1, 3) and (25, 10)? (a) 31 (b) 625 (c) 26 (d) 25
30. 30.What is the midpoint of the line joining (7, 7) and (15, 3)? (a) (11, 5) (b) (22, 10) (c) (4, 2) (d) (5, 11)
31. 31.What is the distance between the points (3, 7) and (15, 2)? (a) 13 (b) 17 (c) 169 (d) 14
32. 32.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
33. 33.What is the distance between the points (6, 7) and (10, 10)? (a) 25 (b) 6 (c) 7 (d) 5
34. 34.In which quadrant does the point (−2, −3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
35. 35.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
36. 36.In which quadrant does the point (9, 9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
37. 37.In which quadrant does the point (9, 5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
38. 38.In which quadrant does the point (3, 9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
39. 39.In which quadrant does the point (6, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
40. 40.What is the midpoint of the line joining (7, 6) and (9, 10)? (a) (9, 8) (b) (16, 16) (c) (8, 8) (d) (1, 2)

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