Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 787 · 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 (5, 6) and (11, 4)? (a) (16, 10) (b) (3, 1) (c) (5, 8) (d) (8, 5)
2. 2.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
3. 3.In which quadrant does the point (4, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
4. 4.In which quadrant does the point (4, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
5. 5.What is the midpoint of the line joining (8, 0) and (10, 6)? (a) (1, 3) (b) (18, 6) (c) (9, 3) (d) (3, 9)
6. 6.What is the midpoint of the line joining (6, 13) and (14, 3)? (a) (10, 8) (b) (8, 10) (c) (20, 16) (d) (4, 5)
7. 7.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
8. 8.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
10. 10.What is the midpoint of the line joining (0, 10) and (2, 12)? (a) (2, 22) (b) (1, 11) (c) (11, 1) (d) (1, 1)
11. 11.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
12. 12.What is the distance between the points (2, 26) and (9, 2)? (a) 25 (b) 26 (c) 31 (d) 625
13. 13.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
14. 14.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
15. 15.In which quadrant does the point (−6, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
16. 16.What is the midpoint of the line joining (5, 5) and (17, 9)? (a) (11, 7) (b) (22, 14) (c) (7, 11) (d) (6, 2)
17. 17.What is the midpoint of the line joining (2, 0) and (14, 8)? (a) (6, 4) (b) (8, 4) (c) (16, 8) (d) (4, 8)
18. 18.What is the distance between the points (8, 18) and (17, 6)? (a) 225 (b) 16 (c) 15 (d) 21
19. 19.What is the midpoint of the line joining (7, 17) and (11, 5)? (a) (2, 6) (b) (18, 22) (c) (9, 11) (d) (11, 9)
20. 20.What is the distance between the points (4, 0) and (28, 7)? (a) 625 (b) 26 (c) 31 (d) 25
21. 21.In which quadrant does the point (7, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
22. 22.In which quadrant does the point (7, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
23. 23.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
24. 24.In which quadrant does the point (−4, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
25. 25.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
26. 26.In which quadrant does the point (3, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
27. 27.In which quadrant does the point (−8, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
28. 28.In which quadrant does the point (−3, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
29. 29.In which quadrant does the point (9, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
30. 30.In which quadrant does the point (8, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
31. 31.What is the midpoint of the line joining (9, 2) and (19, 8)? (a) (14, 5) (b) (5, 14) (c) (5, 3) (d) (28, 10)
32. 32.What is the midpoint of the line joining (0, 0) and (2, 6)? (a) (1, 3) (b) (3, 1) (c) (2, 6) (d) (2, 3)
33. 33.In which quadrant does the point (−2, 7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
34. 34.What is the midpoint of the line joining (2, 20) and (12, 10)? (a) (5, 5) (b) (7, 15) (c) (15, 7) (d) (14, 30)
35. 35.What is the midpoint of the line joining (4, 9) and (8, 7)? (a) (2, 1) (b) (6, 8) (c) (8, 6) (d) (12, 16)
36. 36.What is the midpoint of the line joining (0, 10) and (12, 14)? (a) (12, 24) (b) (6, 2) (c) (6, 12) (d) (12, 6)
37. 37.What is the midpoint of the line joining (10, 12) and (20, 8)? (a) (5, 2) (b) (15, 10) (c) (10, 15) (d) (30, 20)
38. 38.What is the midpoint of the line joining (1, 9) and (3, 11)? (a) (10, 2) (b) (4, 20) (c) (2, 10) (d) (1, 1)
39. 39.What is the distance between the points (7, 3) and (19, 12)? (a) 16 (b) 15 (c) 21 (d) 225
40. 40.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14

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