Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 938 · 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 (4, 19) and (12, 9)? (a) (14, 8) (b) (16, 28) (c) (4, 5) (d) (8, 14)
2. 2.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
3. 3.What is the midpoint of the line joining (6, 8) and (18, 2)? (a) (12, 5) (b) (6, 3) (c) (24, 10) (d) (5, 12)
4. 4.In which quadrant does the point (6, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
5. 5.In which quadrant does the point (−1, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
6. 6.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
7. 7.What is the distance between the points (7, 21) and (16, 9)? (a) 21 (b) 15 (c) 225 (d) 16
8. 8.What is the midpoint of the line joining (8, 16) and (18, 10)? (a) (5, 3) (b) (14, 13) (c) (26, 26) (d) (13, 13)
9. 9.What is the distance between the points (9, 10) and (13, 7)? (a) 25 (b) 6 (c) 5 (d) 7
10. 10.In which quadrant does the point (−3, −4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
11. 11.What is the distance between the points (8, 20) and (20, 4)? (a) 28 (b) 21 (c) 400 (d) 20
12. 12.In which quadrant does the point (3, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
13. 13.What is the midpoint of the line joining (5, 1) and (17, 11)? (a) (11, 6) (b) (6, 11) (c) (6, 5) (d) (22, 12)
14. 14.What is the distance between the points (0, 9) and (4, 6)? (a) 5 (b) 6 (c) 25 (d) 7
15. 15.In which quadrant does the point (−4, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
16. 16.What is the midpoint of the line joining (6, 4) and (12, 10)? (a) (7, 9) (b) (3, 3) (c) (18, 14) (d) (9, 7)
17. 17.What is the midpoint of the line joining (6, 8) and (10, 16)? (a) (2, 4) (b) (8, 12) (c) (16, 24) (d) (12, 8)
18. 18.What is the midpoint of the line joining (10, 17) and (12, 7)? (a) (11, 12) (b) (22, 24) (c) (1, 5) (d) (12, 11)
19. 19.What is the distance between the points (7, 5) and (19, 21)? (a) 400 (b) 21 (c) 28 (d) 20
20. 20.In which quadrant does the point (1, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
21. 21.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
22. 22.In which quadrant does the point (−8, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
23. 23.What is the midpoint of the line joining (6, 8) and (10, 10)? (a) (9, 8) (b) (2, 1) (c) (16, 18) (d) (8, 9)
24. 24.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
25. 25.What is the distance between the points (8, 4) and (14, 12)? (a) 10 (b) 11 (c) 14 (d) 100
26. 26.In which quadrant does the point (7, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
27. 27.In which quadrant does the point (6, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
28. 28.What is the distance between the points (2, 10) and (5, 6)? (a) 5 (b) 7 (c) 25 (d) 6
29. 29.What is the distance between the points (6, 12) and (15, 0)? (a) 21 (b) 15 (c) 225 (d) 16
30. 30.What is the distance between the points (6, 5) and (18, 14)? (a) 16 (b) 15 (c) 225 (d) 21
31. 31.What is the distance between the points (2, 24) and (14, 8)? (a) 20 (b) 400 (c) 21 (d) 28
32. 32.In which quadrant does the point (−3, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
33. 33.What is the midpoint of the line joining (8, 3) and (20, 11)? (a) (7, 14) (b) (6, 4) (c) (14, 7) (d) (28, 14)
34. 34.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
35. 35.What is the distance between the points (7, 8) and (16, 20)? (a) 21 (b) 225 (c) 16 (d) 15
36. 36.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
37. 37.What is the midpoint of the line joining (2, 14) and (12, 10)? (a) (5, 2) (b) (12, 7) (c) (14, 24) (d) (7, 12)
38. 38.What is the midpoint of the line joining (6, 18) and (8, 6)? (a) (1, 6) (b) (7, 12) (c) (12, 7) (d) (14, 24)
39. 39.In which quadrant does the point (1, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
40. 40.What is the distance between the points (8, 3) and (14, 11)? (a) 100 (b) 11 (c) 10 (d) 14

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