Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 145 · 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 (1, 16) and (5, 8)? (a) (6, 24) (b) (12, 3) (c) (2, 4) (d) (3, 12)
2. 2.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
3. 3.What is the midpoint of the line joining (5, 14) and (11, 4)? (a) (3, 5) (b) (16, 18) (c) (9, 8) (d) (8, 9)
4. 4.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
5. 5.What is the distance between the points (0, 5) and (15, 13)? (a) 18 (b) 23 (c) 289 (d) 17
6. 6.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
7. 7.What is the distance between the points (2, 13) and (8, 5)? (a) 10 (b) 14 (c) 11 (d) 100
8. 8.What is the midpoint of the line joining (2, 8) and (10, 12)? (a) (4, 2) (b) (10, 6) (c) (6, 10) (d) (12, 20)
9. 9.What is the midpoint of the line joining (5, 1) and (15, 5)? (a) (20, 6) (b) (10, 3) (c) (3, 10) (d) (5, 2)
10. 10.What is the midpoint of the line joining (6, 17) and (10, 7)? (a) (2, 5) (b) (12, 8) (c) (16, 24) (d) (8, 12)
11. 11.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
12. 12.In which quadrant does the point (−1, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
13. 13.What is the midpoint of the line joining (1, 8) and (3, 14)? (a) (1, 3) (b) (2, 11) (c) (11, 2) (d) (4, 22)
14. 14.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
15. 15.What is the distance between the points (1, 7) and (5, 4)? (a) 5 (b) 25 (c) 6 (d) 7
16. 16.What is the midpoint of the line joining (5, 5) and (13, 9)? (a) (7, 9) (b) (9, 7) (c) (18, 14) (d) (4, 2)
17. 17.In which quadrant does the point (4, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
18. 18.In which quadrant does the point (4, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
19. 19.In which quadrant does the point (−5, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
20. 20.What is the distance between the points (2, 16) and (14, 7)? (a) 225 (b) 21 (c) 15 (d) 16
21. 21.In which quadrant does the point (8, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
22. 22.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
23. 23.What is the midpoint of the line joining (6, 10) and (18, 12)? (a) (24, 22) (b) (6, 1) (c) (11, 12) (d) (12, 11)
24. 24.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)
25. 25.What is the midpoint of the line joining (2, 13) and (10, 9)? (a) (4, 2) (b) (12, 22) (c) (11, 6) (d) (6, 11)
26. 26.What is the midpoint of the line joining (0, 7) and (12, 11)? (a) (12, 18) (b) (9, 6) (c) (6, 9) (d) (6, 2)
27. 27.What is the midpoint of the line joining (6, 14) and (12, 10)? (a) (3, 2) (b) (18, 24) (c) (12, 9) (d) (9, 12)
28. 28.What is the midpoint of the line joining (4, 16) and (14, 4)? (a) (10, 9) (b) (5, 6) (c) (18, 20) (d) (9, 10)
29. 29.What is the distance between the points (0, 12) and (5, 0)? (a) 14 (b) 13 (c) 17 (d) 169
30. 30.What is the distance between the points (9, 17) and (25, 5)? (a) 20 (b) 400 (c) 28 (d) 21
31. 31.What is the midpoint of the line joining (9, 19) and (15, 7)? (a) (12, 13) (b) (3, 6) (c) (24, 26) (d) (13, 12)
32. 32.What is the distance between the points (8, 0) and (23, 8)? (a) 289 (b) 18 (c) 23 (d) 17
33. 33.What is the distance between the points (5, 17) and (17, 8)? (a) 21 (b) 15 (c) 16 (d) 225
34. 34.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
35. 35.In which quadrant does the point (−5, −9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
36. 36.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
37. 37.In which quadrant does the point (−2, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
38. 38.In which quadrant does the point (−8, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
39. 39.In which quadrant does the point (−3, −1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
40. 40.What is the distance between the points (2, 7) and (10, 1)? (a) 11 (b) 10 (c) 14 (d) 100

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