Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 315 · 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 (2, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
2. 2.What is the midpoint of the line joining (9, 9) and (15, 21)? (a) (12, 15) (b) (24, 30) (c) (15, 12) (d) (3, 6)
3. 3.In which quadrant does the point (2, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
4. 4.What is the midpoint of the line joining (9, 5) and (21, 1)? (a) (6, 2) (b) (15, 3) (c) (3, 15) (d) (30, 6)
5. 5.In which quadrant does the point (−6, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
6. 6.What is the midpoint of the line joining (4, 20) and (14, 8)? (a) (9, 14) (b) (14, 9) (c) (18, 28) (d) (5, 6)
7. 7.What is the midpoint of the line joining (10, 8) and (12, 12)? (a) (22, 20) (b) (10, 11) (c) (1, 2) (d) (11, 10)
8. 8.In which quadrant does the point (2, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
9. 9.What is the distance between the points (1, 1) and (17, 13)? (a) 400 (b) 28 (c) 20 (d) 21
10. 10.What is the distance between the points (4, 7) and (12, 22)? (a) 18 (b) 289 (c) 17 (d) 23
11. 11.What is the distance between the points (5, 11) and (13, 5)? (a) 10 (b) 11 (c) 14 (d) 100
12. 12.In which quadrant does the point (9, 7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
13. 13.In which quadrant does the point (9, −7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
14. 14.What is the distance between the points (4, 21) and (16, 5)? (a) 21 (b) 400 (c) 28 (d) 20
15. 15.In which quadrant does the point (4, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
16. 16.What is the midpoint of the line joining (5, 2) and (11, 10)? (a) (3, 4) (b) (16, 12) (c) (8, 6) (d) (6, 8)
17. 17.What is the distance between the points (7, 9) and (13, 1)? (a) 11 (b) 10 (c) 100 (d) 14
18. 18.In which quadrant does the point (9, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
19. 19.What is the distance between the points (0, 26) and (7, 2)? (a) 26 (b) 625 (c) 25 (d) 31
20. 20.In which quadrant does the point (6, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
21. 21.What is the distance between the points (5, 20) and (10, 8)? (a) 169 (b) 13 (c) 14 (d) 17
22. 22.In which quadrant does the point (−2, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
23. 23.In which quadrant does the point (−7, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
24. 24.What is the distance between the points (8, 20) and (13, 8)? (a) 14 (b) 169 (c) 17 (d) 13
25. 25.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
26. 26.What is the distance between the points (3, 24) and (15, 8)? (a) 21 (b) 28 (c) 400 (d) 20
27. 27.In which quadrant does the point (−6, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
28. 28.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
29. 29.What is the midpoint of the line joining (6, 4) and (8, 2)? (a) (7, 3) (b) (3, 7) (c) (1, 1) (d) (14, 6)
30. 30.In which quadrant does the point (5, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
31. 31.In which quadrant does the point (−4, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
32. 32.What is the midpoint of the line joining (9, 8) and (19, 4)? (a) (5, 2) (b) (6, 14) (c) (14, 6) (d) (28, 12)
33. 33.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
34. 34.What is the distance between the points (4, 18) and (20, 6)? (a) 28 (b) 400 (c) 21 (d) 20
35. 35.What is the distance between the points (6, 1) and (30, 8)? (a) 625 (b) 25 (c) 26 (d) 31
36. 36.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
37. 37.What is the midpoint of the line joining (9, 0) and (21, 8)? (a) (6, 4) (b) (4, 15) (c) (15, 4) (d) (30, 8)
38. 38.In which quadrant does the point (−4, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
39. 39.In which quadrant does the point (1, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
40. 40.In which quadrant does the point (3, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant

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