Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 216 · 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 (7, 5) and (15, 20)? (a) 17 (b) 289 (c) 23 (d) 18
2. 2.What is the midpoint of the line joining (3, 3) and (7, 15)? (a) (9, 5) (b) (10, 18) (c) (2, 6) (d) (5, 9)
3. 3.What is the distance between the points (2, 4) and (5, 8)? (a) 5 (b) 6 (c) 25 (d) 7
4. 4.In which quadrant does the point (9, −4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
5. 5.What is the distance between the points (1, 2) and (5, 5)? (a) 25 (b) 5 (c) 6 (d) 7
6. 6.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
7. 7.In which quadrant does the point (9, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
8. 8.In which quadrant does the point (1, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
9. 9.What is the midpoint of the line joining (1, 7) and (11, 1)? (a) (5, 3) (b) (12, 8) (c) (4, 6) (d) (6, 4)
10. 10.In which quadrant does the point (−5, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
11. 11.What is the midpoint of the line joining (1, 12) and (13, 4)? (a) (14, 16) (b) (6, 4) (c) (7, 8) (d) (8, 7)
12. 12.What is the midpoint of the line joining (0, 0) and (4, 2)? (a) (2, 1) (b) (3, 1) (c) (4, 2) (d) (1, 2)
13. 13.What is the distance between the points (2, 23) and (10, 8)? (a) 289 (b) 18 (c) 23 (d) 17
14. 14.In which quadrant does the point (−1, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
15. 15.In which quadrant does the point (−9, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
16. 16.What is the midpoint of the line joining (5, 14) and (11, 4)? (a) (16, 18) (b) (8, 9) (c) (9, 8) (d) (3, 5)
17. 17.In which quadrant does the point (−8, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
18. 18.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
19. 19.In which quadrant does the point (5, −8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
20. 20.What is the distance between the points (8, 1) and (12, 4)? (a) 5 (b) 6 (c) 7 (d) 25
21. 21.In which quadrant does the point (−9, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
22. 22.What is the midpoint of the line joining (5, 7) and (7, 17)? (a) (1, 5) (b) (12, 24) (c) (6, 12) (d) (12, 6)
23. 23.In which quadrant does the point (−2, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
24. 24.In which quadrant does the point (5, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
25. 25.In which quadrant does the point (−8, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
26. 26.What is the distance between the points (1, 8) and (7, 16)? (a) 11 (b) 10 (c) 100 (d) 14
27. 27.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
28. 28.What is the distance between the points (9, 5) and (13, 2)? (a) 5 (b) 6 (c) 7 (d) 25
29. 29.What is the distance between the points (3, 2) and (9, 10)? (a) 100 (b) 14 (c) 11 (d) 10
30. 30.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
31. 31.What is the midpoint of the line joining (3, 2) and (15, 0)? (a) (18, 2) (b) (9, 1) (c) (1, 9) (d) (6, 1)
32. 32.What is the midpoint of the line joining (2, 4) and (14, 16)? (a) (8, 10) (b) (16, 20) (c) (6, 6) (d) (10, 8)
33. 33.What is the distance between the points (3, 13) and (19, 1)? (a) 20 (b) 21 (c) 400 (d) 28
34. 34.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
35. 35.In which quadrant does the point (−3, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
36. 36.What is the midpoint of the line joining (8, 2) and (10, 4)? (a) (3, 9) (b) (1, 1) (c) (9, 3) (d) (18, 6)
37. 37.What is the distance between the points (5, 4) and (10, 16)? (a) 169 (b) 13 (c) 14 (d) 17
38. 38.In which quadrant does the point (−2, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
39. 39.What is the midpoint of the line joining (9, 17) and (21, 7)? (a) (12, 15) (b) (30, 24) (c) (15, 12) (d) (6, 5)
40. 40.What is the distance between the points (9, 12) and (15, 4)? (a) 14 (b) 11 (c) 100 (d) 10

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