Coordinate Geometry Worksheet for Maths Olympiad

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

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