Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 258 · 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 midpoint of the line joining (0, 10) and (8, 2)? (a) (4, 4) (b) (6, 4) (c) (4, 6) (d) (8, 12)
2. 2.In which quadrant does the point (−9, −9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
3. 3.What is the midpoint of the line joining (9, 0) and (21, 4)? (a) (15, 2) (b) (6, 2) (c) (2, 15) (d) (30, 4)
4. 4.In which quadrant does the point (5, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
5. 5.What is the midpoint of the line joining (9, 8) and (21, 6)? (a) (6, 1) (b) (30, 14) (c) (7, 15) (d) (15, 7)
6. 6.What is the midpoint of the line joining (1, 1) and (9, 7)? (a) (4, 5) (b) (5, 4) (c) (10, 8) (d) (4, 3)
7. 7.In which quadrant does the point (3, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
8. 8.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
9. 9.What is the distance between the points (6, 7) and (18, 12)? (a) 17 (b) 13 (c) 14 (d) 169
10. 10.What is the midpoint of the line joining (10, 8) and (14, 12)? (a) (24, 20) (b) (2, 2) (c) (12, 10) (d) (10, 12)
11. 11.In which quadrant does the point (−2, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
12. 12.What is the distance between the points (3, 7) and (10, 31)? (a) 26 (b) 25 (c) 31 (d) 625
13. 13.What is the distance between the points (1, 16) and (25, 9)? (a) 31 (b) 25 (c) 625 (d) 26
14. 14.What is the midpoint of the line joining (10, 12) and (22, 10)? (a) (16, 11) (b) (11, 16) (c) (32, 22) (d) (6, 1)
15. 15.What is the distance between the points (5, 14) and (11, 6)? (a) 14 (b) 11 (c) 10 (d) 100
16. 16.What is the distance between the points (2, 8) and (14, 17)? (a) 16 (b) 15 (c) 21 (d) 225
17. 17.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 21 (d) 225
18. 18.What is the distance between the points (1, 15) and (10, 3)? (a) 225 (b) 16 (c) 15 (d) 21
19. 19.In which quadrant does the point (9, 7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
20. 20.What is the midpoint of the line joining (3, 18) and (9, 10)? (a) (3, 4) (b) (12, 28) (c) (14, 6) (d) (6, 14)
21. 21.In which quadrant does the point (−9, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
22. 22.In which quadrant does the point (−3, −2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
23. 23.In which quadrant does the point (−5, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
24. 24.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
25. 25.What is the midpoint of the line joining (10, 14) and (20, 6)? (a) (10, 15) (b) (5, 4) (c) (30, 20) (d) (15, 10)
26. 26.What is the distance between the points (1, 11) and (7, 3)? (a) 100 (b) 14 (c) 11 (d) 10
27. 27.In which quadrant does the point (1, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
28. 28.What is the distance between the points (8, 10) and (12, 7)? (a) 6 (b) 5 (c) 7 (d) 25
29. 29.In which quadrant does the point (8, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
30. 30.In which quadrant does the point (−6, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
31. 31.What is the distance between the points (4, 7) and (8, 10)? (a) 6 (b) 25 (c) 5 (d) 7
32. 32.What is the midpoint of the line joining (8, 7) and (20, 3)? (a) (14, 5) (b) (6, 2) (c) (28, 10) (d) (5, 14)
33. 33.In which quadrant does the point (−4, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
34. 34.What is the midpoint of the line joining (7, 12) and (19, 6)? (a) (6, 3) (b) (9, 13) (c) (26, 18) (d) (13, 9)
35. 35.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
36. 36.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
37. 37.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
38. 38.In which quadrant does the point (7, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
39. 39.What is the midpoint of the line joining (5, 4) and (15, 10)? (a) (10, 7) (b) (5, 3) (c) (20, 14) (d) (7, 10)
40. 40.In which quadrant does the point (−9, −5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant

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