Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 661 · 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.In which quadrant does the point (9, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
2. 2.In which quadrant does the point (−4, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
3. 3.What is the midpoint of the line joining (1, 12) and (7, 4)? (a) (8, 16) (b) (4, 8) (c) (3, 4) (d) (8, 4)
4. 4.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
5. 5.In which quadrant does the point (1, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
6. 6.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
7. 7.What is the distance between the points (0, 13) and (3, 9)? (a) 25 (b) 6 (c) 7 (d) 5
8. 8.What is the distance between the points (6, 5) and (18, 14)? (a) 15 (b) 21 (c) 16 (d) 225
9. 9.In which quadrant does the point (6, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
10. 10.What is the distance between the points (9, 21) and (21, 5)? (a) 400 (b) 20 (c) 28 (d) 21
11. 11.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
12. 12.What is the distance between the points (6, 28) and (13, 4)? (a) 26 (b) 31 (c) 625 (d) 25
13. 13.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
14. 14.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
15. 15.In which quadrant does the point (−4, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
16. 16.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
17. 17.What is the midpoint of the line joining (3, 0) and (9, 2)? (a) (6, 1) (b) (12, 2) (c) (3, 1) (d) (1, 6)
18. 18.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
19. 19.What is the distance between the points (4, 9) and (13, 21)? (a) 16 (b) 21 (c) 225 (d) 15
20. 20.What is the midpoint of the line joining (2, 3) and (6, 11)? (a) (2, 4) (b) (8, 14) (c) (7, 4) (d) (4, 7)
21. 21.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
22. 22.What is the midpoint of the line joining (1, 11) and (5, 1)? (a) (2, 5) (b) (6, 12) (c) (6, 3) (d) (3, 6)
23. 23.In which quadrant does the point (−9, −5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
24. 24.What is the midpoint of the line joining (7, 4) and (19, 6)? (a) (6, 1) (b) (26, 10) (c) (5, 13) (d) (13, 5)
25. 25.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
26. 26.What is the midpoint of the line joining (2, 2) and (8, 14)? (a) (5, 8) (b) (10, 16) (c) (8, 5) (d) (3, 6)
27. 27.In which quadrant does the point (−9, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
28. 28.What is the distance between the points (1, 6) and (5, 3)? (a) 6 (b) 25 (c) 5 (d) 7
29. 29.In which quadrant does the point (−8, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
30. 30.In which quadrant does the point (2, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
31. 31.What is the midpoint of the line joining (3, 6) and (9, 0)? (a) (3, 3) (b) (3, 6) (c) (6, 3) (d) (12, 6)
32. 32.What is the midpoint of the line joining (3, 10) and (5, 16)? (a) (13, 4) (b) (8, 26) (c) (1, 3) (d) (4, 13)
33. 33.What is the midpoint of the line joining (8, 4) and (18, 8)? (a) (26, 12) (b) (5, 2) (c) (13, 6) (d) (6, 13)
34. 34.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
35. 35.In which quadrant does the point (2, −1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
36. 36.What is the midpoint of the line joining (9, 12) and (13, 10)? (a) (2, 1) (b) (12, 11) (c) (22, 22) (d) (11, 11)
37. 37.What is the distance between the points (9, 9) and (33, 16)? (a) 625 (b) 31 (c) 26 (d) 25
38. 38.What is the distance between the points (6, 0) and (30, 7)? (a) 25 (b) 31 (c) 26 (d) 625
39. 39.What is the midpoint of the line joining (1, 13) and (11, 1)? (a) (12, 14) (b) (7, 6) (c) (5, 6) (d) (6, 7)
40. 40.What is the midpoint of the line joining (10, 5) and (12, 15)? (a) (11, 10) (b) (10, 11) (c) (1, 5) (d) (22, 20)

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