Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 477 · 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 distance between the points (9, 7) and (24, 15)? (a) 289 (b) 18 (c) 23 (d) 17
2. 2.What is the midpoint of the line joining (3, 2) and (15, 4)? (a) (9, 3) (b) (18, 6) (c) (3, 9) (d) (6, 1)
3. 3.What is the midpoint of the line joining (8, 9) and (10, 3)? (a) (18, 12) (b) (1, 3) (c) (6, 9) (d) (9, 6)
4. 4.What is the distance between the points (1, 3) and (13, 8)? (a) 169 (b) 13 (c) 14 (d) 17
5. 5.What is the midpoint of the line joining (2, 5) and (6, 13)? (a) (2, 4) (b) (4, 9) (c) (8, 18) (d) (9, 4)
6. 6.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
7. 7.What is the midpoint of the line joining (7, 18) and (17, 10)? (a) (24, 28) (b) (5, 4) (c) (12, 14) (d) (14, 12)
8. 8.What is the midpoint of the line joining (10, 2) and (14, 12)? (a) (7, 12) (b) (24, 14) (c) (2, 5) (d) (12, 7)
9. 9.What is the distance between the points (4, 1) and (16, 6)? (a) 17 (b) 169 (c) 14 (d) 13
10. 10.What is the distance between the points (4, 19) and (20, 7)? (a) 28 (b) 400 (c) 21 (d) 20
11. 11.What is the midpoint of the line joining (7, 3) and (17, 1)? (a) (12, 2) (b) (5, 1) (c) (2, 12) (d) (24, 4)
12. 12.In which quadrant does the point (3, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
13. 13.What is the midpoint of the line joining (0, 7) and (10, 3)? (a) (5, 5) (b) (10, 10) (c) (6, 5) (d) (5, 2)
14. 14.What is the midpoint of the line joining (9, 13) and (15, 9)? (a) (3, 2) (b) (11, 12) (c) (12, 11) (d) (24, 22)
15. 15.What is the midpoint of the line joining (8, 10) and (20, 4)? (a) (6, 3) (b) (7, 14) (c) (28, 14) (d) (14, 7)
16. 16.What is the distance between the points (3, 20) and (12, 8)? (a) 225 (b) 16 (c) 21 (d) 15
17. 17.In which quadrant does the point (−4, 2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
18. 18.What is the distance between the points (0, 19) and (12, 3)? (a) 400 (b) 28 (c) 21 (d) 20
19. 19.In which quadrant does the point (2, −2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
20. 20.What is the distance between the points (0, 0) and (12, 9)? (a) 225 (b) 15 (c) 21 (d) 16
21. 21.In which quadrant does the point (6, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
22. 22.In which quadrant does the point (2, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
23. 23.What is the midpoint of the line joining (9, 12) and (11, 2)? (a) (1, 5) (b) (20, 14) (c) (7, 10) (d) (10, 7)
24. 24.In which quadrant does the point (9, −5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
25. 25.In which quadrant does the point (4, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
26. 26.In which quadrant does the point (−5, −1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
27. 27.In which quadrant does the point (−2, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
28. 28.In which quadrant does the point (4, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
29. 29.In which quadrant does the point (4, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
30. 30.What is the midpoint of the line joining (8, 6) and (14, 10)? (a) (22, 16) (b) (8, 11) (c) (11, 8) (d) (3, 2)
31. 31.What is the distance between the points (5, 33) and (12, 9)? (a) 625 (b) 26 (c) 31 (d) 25
32. 32.What is the distance between the points (5, 11) and (11, 3)? (a) 10 (b) 14 (c) 100 (d) 11
33. 33.In which quadrant does the point (7, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
34. 34.What is the distance between the points (4, 10) and (16, 5)? (a) 17 (b) 169 (c) 13 (d) 14
35. 35.In which quadrant does the point (−5, 6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
36. 36.In which quadrant does the point (−6, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
37. 37.What is the distance between the points (6, 1) and (12, 9)? (a) 10 (b) 14 (c) 100 (d) 11
38. 38.What is the distance between the points (0, 16) and (12, 7)? (a) 225 (b) 16 (c) 21 (d) 15
39. 39.What is the distance between the points (4, 12) and (10, 4)? (a) 14 (b) 100 (c) 10 (d) 11
40. 40.In which quadrant does the point (−2, −2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant

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