Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 592 · 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 (8, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
2. 2.In which quadrant does the point (8, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
3. 3.What is the midpoint of the line joining (9, 1) and (11, 5)? (a) (20, 6) (b) (10, 3) (c) (3, 10) (d) (1, 2)
4. 4.In which quadrant does the point (−8, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
5. 5.What is the distance between the points (0, 8) and (12, 24)? (a) 21 (b) 28 (c) 400 (d) 20
6. 6.What is the distance between the points (1, 0) and (25, 7)? (a) 625 (b) 25 (c) 26 (d) 31
7. 7.In which quadrant does the point (−6, −8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
8. 8.What is the distance between the points (0, 1) and (12, 10)? (a) 21 (b) 225 (c) 16 (d) 15
9. 9.What is the distance between the points (5, 9) and (14, 21)? (a) 16 (b) 15 (c) 21 (d) 225
10. 10.In which quadrant does the point (7, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
12. 12.In which quadrant does the point (−3, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
13. 13.What is the midpoint of the line joining (9, 9) and (21, 15)? (a) (30, 24) (b) (6, 3) (c) (15, 12) (d) (12, 15)
14. 14.In which quadrant does the point (3, −7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
15. 15.In which quadrant does the point (−1, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
16. 16.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
17. 17.What is the midpoint of the line joining (9, 11) and (15, 3)? (a) (12, 7) (b) (24, 14) (c) (3, 4) (d) (7, 12)
18. 18.What is the distance between the points (1, 12) and (9, 6)? (a) 100 (b) 11 (c) 10 (d) 14
19. 19.What is the midpoint of the line joining (10, 11) and (20, 9)? (a) (10, 15) (b) (5, 1) (c) (30, 20) (d) (15, 10)
20. 20.What is the midpoint of the line joining (2, 6) and (4, 12)? (a) (1, 3) (b) (3, 9) (c) (6, 18) (d) (9, 3)
21. 21.What is the midpoint of the line joining (2, 15) and (10, 9)? (a) (12, 24) (b) (6, 12) (c) (4, 3) (d) (12, 6)
22. 22.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
23. 23.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
24. 24.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
25. 25.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
26. 26.In which quadrant does the point (−1, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
27. 27.In which quadrant does the point (−7, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
28. 28.What is the distance between the points (5, 2) and (20, 10)? (a) 17 (b) 23 (c) 289 (d) 18
29. 29.What is the distance between the points (0, 3) and (6, 11)? (a) 14 (b) 10 (c) 11 (d) 100
30. 30.What is the distance between the points (4, 15) and (12, 9)? (a) 14 (b) 10 (c) 100 (d) 11
31. 31.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
32. 32.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
33. 33.In which quadrant does the point (−2, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
34. 34.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
35. 35.What is the midpoint of the line joining (7, 2) and (9, 8)? (a) (1, 3) (b) (16, 10) (c) (5, 8) (d) (8, 5)
36. 36.What is the midpoint of the line joining (5, 4) and (13, 6)? (a) (18, 10) (b) (5, 9) (c) (9, 5) (d) (4, 1)
37. 37.What is the distance between the points (3, 5) and (10, 29)? (a) 26 (b) 625 (c) 25 (d) 31
38. 38.What is the distance between the points (7, 7) and (19, 12)? (a) 13 (b) 17 (c) 14 (d) 169
39. 39.What is the midpoint of the line joining (4, 7) and (16, 5)? (a) (6, 1) (b) (6, 10) (c) (20, 12) (d) (10, 6)
40. 40.In which quadrant does the point (−1, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant

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