Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 284 · 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, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
2. 2.In which quadrant does the point (2, −8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
3. 3.What is the midpoint of the line joining (10, 18) and (14, 10)? (a) (14, 12) (b) (2, 4) (c) (24, 28) (d) (12, 14)
4. 4.In which quadrant does the point (−7, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
5. 5.What is the distance between the points (0, 6) and (4, 9)? (a) 6 (b) 5 (c) 25 (d) 7
6. 6.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
7. 7.What is the distance between the points (2, 7) and (14, 2)? (a) 17 (b) 169 (c) 14 (d) 13
8. 8.What is the distance between the points (1, 9) and (5, 12)? (a) 25 (b) 6 (c) 5 (d) 7
9. 9.What is the distance between the points (7, 5) and (19, 21)? (a) 400 (b) 28 (c) 21 (d) 20
10. 10.What is the midpoint of the line joining (2, 5) and (6, 1)? (a) (2, 2) (b) (3, 4) (c) (8, 6) (d) (4, 3)
11. 11.What is the midpoint of the line joining (2, 6) and (10, 10)? (a) (6, 8) (b) (12, 16) (c) (8, 6) (d) (4, 2)
12. 12.What is the midpoint of the line joining (0, 9) and (10, 1)? (a) (10, 10) (b) (5, 4) (c) (5, 5) (d) (6, 5)
13. 13.In which quadrant does the point (8, 6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
14. 14.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
15. 15.What is the midpoint of the line joining (8, 5) and (18, 15)? (a) (26, 20) (b) (13, 10) (c) (10, 13) (d) (5, 5)
16. 16.In which quadrant does the point (−4, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
17. 17.In which quadrant does the point (7, −8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
18. 18.In which quadrant does the point (−3, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
19. 19.What is the distance between the points (1, 17) and (13, 1)? (a) 28 (b) 20 (c) 21 (d) 400
20. 20.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
21. 21.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
22. 22.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
23. 23.What is the midpoint of the line joining (2, 6) and (14, 10)? (a) (16, 16) (b) (9, 8) (c) (8, 8) (d) (6, 2)
24. 24.In which quadrant does the point (8, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
25. 25.What is the distance between the points (3, 8) and (9, 0)? (a) 100 (b) 11 (c) 14 (d) 10
26. 26.What is the midpoint of the line joining (1, 13) and (9, 9)? (a) (10, 22) (b) (5, 11) (c) (11, 5) (d) (4, 2)
27. 27.In which quadrant does the point (4, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
28. 28.What is the distance between the points (1, 6) and (13, 11)? (a) 169 (b) 14 (c) 13 (d) 17
29. 29.In which quadrant does the point (−1, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
30. 30.What is the distance between the points (2, 15) and (10, 9)? (a) 100 (b) 14 (c) 11 (d) 10
31. 31.What is the distance between the points (6, 9) and (14, 24)? (a) 18 (b) 17 (c) 289 (d) 23
32. 32.What is the distance between the points (2, 15) and (26, 8)? (a) 26 (b) 25 (c) 625 (d) 31
33. 33.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
34. 34.In which quadrant does the point (4, −5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
35. 35.What is the midpoint of the line joining (8, 8) and (18, 0)? (a) (4, 13) (b) (5, 4) (c) (26, 8) (d) (13, 4)
36. 36.What is the distance between the points (5, 4) and (10, 16)? (a) 17 (b) 14 (c) 13 (d) 169
37. 37.What is the distance between the points (7, 28) and (14, 4)? (a) 31 (b) 26 (c) 25 (d) 625
38. 38.What is the distance between the points (3, 4) and (15, 13)? (a) 225 (b) 21 (c) 15 (d) 16
39. 39.In which quadrant does the point (−9, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
40. 40.What is the midpoint of the line joining (0, 4) and (4, 2)? (a) (4, 6) (b) (2, 3) (c) (2, 1) (d) (3, 2)

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