Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 312 · 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, 6) and (14, 30)? (a) 625 (b) 26 (c) 25 (d) 31
2. 2.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
3. 3.In which quadrant does the point (−8, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
4. 4.What is the midpoint of the line joining (8, 1) and (10, 9)? (a) (18, 10) (b) (5, 9) (c) (1, 4) (d) (9, 5)
5. 5.What is the distance between the points (4, 1) and (19, 9)? (a) 23 (b) 18 (c) 17 (d) 289
6. 6.What is the midpoint of the line joining (10, 19) and (18, 7)? (a) (13, 14) (b) (28, 26) (c) (14, 13) (d) (4, 6)
7. 7.In which quadrant does the point (2, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
8. 8.What is the midpoint of the line joining (0, 6) and (4, 18)? (a) (4, 24) (b) (2, 12) (c) (12, 2) (d) (2, 6)
9. 9.What is the distance between the points (9, 2) and (17, 17)? (a) 289 (b) 23 (c) 18 (d) 17
10. 10.What is the distance between the points (1, 12) and (6, 0)? (a) 17 (b) 169 (c) 14 (d) 13
11. 11.What is the distance between the points (7, 12) and (10, 8)? (a) 25 (b) 7 (c) 5 (d) 6
12. 12.In which quadrant does the point (−9, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
13. 13.In which quadrant does the point (−8, 3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
14. 14.In which quadrant does the point (−5, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
15. 15.What is the midpoint of the line joining (3, 22) and (7, 10)? (a) (5, 16) (b) (10, 32) (c) (16, 5) (d) (2, 6)
16. 16.What is the distance between the points (0, 14) and (12, 9)? (a) 17 (b) 14 (c) 13 (d) 169
17. 17.What is the midpoint of the line joining (10, 6) and (20, 8)? (a) (7, 15) (b) (5, 1) (c) (15, 7) (d) (30, 14)
18. 18.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
19. 19.In which quadrant does the point (−1, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
20. 20.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
21. 21.In which quadrant does the point (7, −6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
22. 22.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 14 (d) 169
23. 23.In which quadrant does the point (9, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
24. 24.In which quadrant does the point (−5, −6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
25. 25.In which quadrant does the point (−1, −9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
26. 26.What is the midpoint of the line joining (3, 15) and (11, 3)? (a) (4, 6) (b) (7, 9) (c) (14, 18) (d) (9, 7)
27. 27.What is the midpoint of the line joining (0, 9) and (2, 13)? (a) (2, 22) (b) (1, 2) (c) (1, 11) (d) (11, 1)
28. 28.What is the distance between the points (4, 6) and (10, 14)? (a) 10 (b) 11 (c) 100 (d) 14
29. 29.What is the distance between the points (7, 20) and (16, 8)? (a) 15 (b) 21 (c) 16 (d) 225
30. 30.What is the distance between the points (9, 5) and (14, 17)? (a) 17 (b) 14 (c) 169 (d) 13
31. 31.What is the distance between the points (7, 4) and (15, 10)? (a) 10 (b) 14 (c) 100 (d) 11
32. 32.What is the midpoint of the line joining (6, 10) and (8, 2)? (a) (1, 4) (b) (6, 7) (c) (14, 12) (d) (7, 6)
33. 33.What is the midpoint of the line joining (2, 1) and (12, 5)? (a) (14, 6) (b) (5, 2) (c) (7, 3) (d) (3, 7)
34. 34.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
35. 35.What is the distance between the points (9, 0) and (21, 16)? (a) 400 (b) 20 (c) 21 (d) 28
36. 36.What is the distance between the points (3, 0) and (11, 6)? (a) 10 (b) 14 (c) 11 (d) 100
37. 37.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
38. 38.What is the distance between the points (4, 11) and (28, 4)? (a) 26 (b) 625 (c) 25 (d) 31
39. 39.What is the distance between the points (5, 9) and (21, 21)? (a) 28 (b) 20 (c) 400 (d) 21
40. 40.What is the midpoint of the line joining (8, 6) and (16, 10)? (a) (4, 2) (b) (8, 12) (c) (12, 8) (d) (24, 16)

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