Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 913 · 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 (−7, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
2. 2.What is the midpoint of the line joining (0, 21) and (2, 9)? (a) (1, 6) (b) (1, 15) (c) (15, 1) (d) (2, 30)
3. 3.What is the midpoint of the line joining (9, 0) and (21, 4)? (a) (2, 15) (b) (6, 2) (c) (15, 2) (d) (30, 4)
4. 4.What is the distance between the points (6, 8) and (18, 24)? (a) 20 (b) 400 (c) 28 (d) 21
5. 5.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
6. 6.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
8. 8.What is the midpoint of the line joining (1, 2) and (3, 6)? (a) (4, 2) (b) (2, 4) (c) (4, 8) (d) (1, 2)
9. 9.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
10. 10.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
11. 11.What is the midpoint of the line joining (7, 1) and (19, 13)? (a) (7, 13) (b) (6, 6) (c) (26, 14) (d) (13, 7)
12. 12.What is the distance between the points (5, 1) and (21, 13)? (a) 20 (b) 21 (c) 28 (d) 400
13. 13.What is the midpoint of the line joining (3, 6) and (13, 4)? (a) (16, 10) (b) (5, 1) (c) (8, 5) (d) (5, 8)
14. 14.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
15. 15.In which quadrant does the point (−4, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
16. 16.In which quadrant does the point (−6, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
17. 17.What is the midpoint of the line joining (8, 3) and (20, 13)? (a) (6, 5) (b) (8, 14) (c) (28, 16) (d) (14, 8)
18. 18.In which quadrant does the point (9, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
19. 19.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
20. 20.What is the distance between the points (6, 8) and (21, 16)? (a) 23 (b) 18 (c) 289 (d) 17
21. 21.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
22. 22.What is the midpoint of the line joining (7, 10) and (11, 14)? (a) (18, 24) (b) (2, 2) (c) (12, 9) (d) (9, 12)
23. 23.What is the midpoint of the line joining (0, 0) and (6, 6)? (a) (4, 3) (b) (6, 6) (c) (3, 3) (d) (3, 4)
24. 24.In which quadrant does the point (−3, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
25. 25.What is the distance between the points (3, 14) and (12, 2)? (a) 225 (b) 15 (c) 21 (d) 16
26. 26.In which quadrant does the point (−8, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
27. 27.What is the distance between the points (0, 14) and (9, 2)? (a) 225 (b) 16 (c) 21 (d) 15
28. 28.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
29. 29.What is the distance between the points (0, 16) and (12, 0)? (a) 21 (b) 400 (c) 28 (d) 20
30. 30.What is the distance between the points (7, 8) and (22, 0)? (a) 18 (b) 17 (c) 289 (d) 23
31. 31.In which quadrant does the point (4, −1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
32. 32.In which quadrant does the point (1, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
33. 33.What is the distance between the points (7, 4) and (23, 16)? (a) 28 (b) 400 (c) 21 (d) 20
34. 34.What is the midpoint of the line joining (4, 0) and (8, 12)? (a) (12, 12) (b) (7, 6) (c) (6, 6) (d) (2, 6)
35. 35.What is the distance between the points (9, 6) and (16, 30)? (a) 31 (b) 625 (c) 26 (d) 25
36. 36.What is the distance between the points (3, 8) and (8, 20)? (a) 169 (b) 14 (c) 17 (d) 13
37. 37.What is the distance between the points (2, 5) and (18, 17)? (a) 28 (b) 21 (c) 20 (d) 400
38. 38.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
39. 39.What is the distance between the points (1, 5) and (13, 10)? (a) 17 (b) 14 (c) 13 (d) 169
40. 40.What is the midpoint of the line joining (7, 14) and (15, 10)? (a) (12, 11) (b) (22, 24) (c) (4, 2) (d) (11, 12)

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