Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 423 · 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 (0, 2) and (4, 8)? (a) (2, 3) (b) (2, 5) (c) (5, 2) (d) (4, 10)
2. 2.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
3. 3.What is the distance between the points (4, 2) and (12, 17)? (a) 23 (b) 289 (c) 18 (d) 17
4. 4.In which quadrant does the point (5, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
5. 5.In which quadrant does the point (8, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
6. 6.What is the midpoint of the line joining (7, 13) and (15, 1)? (a) (22, 14) (b) (4, 6) (c) (11, 7) (d) (7, 11)
7. 7.What is the distance between the points (5, 16) and (20, 8)? (a) 17 (b) 289 (c) 18 (d) 23
8. 8.What is the distance between the points (6, 9) and (21, 17)? (a) 289 (b) 18 (c) 17 (d) 23
9. 9.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
10. 10.What is the midpoint of the line joining (8, 14) and (18, 8)? (a) (5, 3) (b) (13, 11) (c) (11, 13) (d) (26, 22)
11. 11.What is the distance between the points (1, 8) and (7, 16)? (a) 14 (b) 10 (c) 11 (d) 100
12. 12.What is the distance between the points (7, 1) and (16, 13)? (a) 225 (b) 21 (c) 15 (d) 16
13. 13.What is the midpoint of the line joining (2, 18) and (14, 10)? (a) (6, 4) (b) (14, 8) (c) (16, 28) (d) (8, 14)
14. 14.In which quadrant does the point (−2, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
15. 15.In which quadrant does the point (−3, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
16. 16.What is the midpoint of the line joining (1, 3) and (3, 5)? (a) (4, 8) (b) (4, 2) (c) (2, 4) (d) (1, 1)
17. 17.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
18. 18.What is the distance between the points (7, 7) and (19, 16)? (a) 21 (b) 225 (c) 16 (d) 15
19. 19.In which quadrant does the point (−8, −8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
20. 20.What is the midpoint of the line joining (0, 5) and (8, 7)? (a) (6, 4) (b) (4, 1) (c) (8, 12) (d) (4, 6)
21. 21.What is the distance between the points (2, 0) and (8, 8)? (a) 14 (b) 10 (c) 100 (d) 11
22. 22.What is the midpoint of the line joining (5, 0) and (7, 10)? (a) (6, 5) (b) (5, 6) (c) (1, 5) (d) (12, 10)
23. 23.What is the midpoint of the line joining (5, 9) and (15, 3)? (a) (10, 6) (b) (20, 12) (c) (6, 10) (d) (5, 3)
24. 24.In which quadrant does the point (7, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
25. 25.What is the midpoint of the line joining (2, 4) and (6, 12)? (a) (2, 4) (b) (4, 8) (c) (8, 16) (d) (8, 4)
26. 26.What is the midpoint of the line joining (4, 9) and (16, 13)? (a) (11, 10) (b) (6, 2) (c) (20, 22) (d) (10, 11)
27. 27.In which quadrant does the point (7, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
28. 28.What is the midpoint of the line joining (2, 10) and (12, 0)? (a) (5, 5) (b) (14, 10) (c) (5, 7) (d) (7, 5)
29. 29.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
30. 30.What is the distance between the points (7, 6) and (13, 14)? (a) 14 (b) 10 (c) 11 (d) 100
31. 31.In which quadrant does the point (−3, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
32. 32.What is the distance between the points (3, 14) and (12, 2)? (a) 16 (b) 225 (c) 21 (d) 15
33. 33.What is the midpoint of the line joining (9, 0) and (19, 10)? (a) (5, 5) (b) (28, 10) (c) (5, 14) (d) (14, 5)
34. 34.What is the midpoint of the line joining (1, 6) and (13, 16)? (a) (6, 5) (b) (14, 22) (c) (11, 7) (d) (7, 11)
35. 35.What is the midpoint of the line joining (8, 9) and (12, 19)? (a) (10, 14) (b) (20, 28) (c) (14, 10) (d) (2, 5)
36. 36.What is the midpoint of the line joining (3, 14) and (7, 2)? (a) (5, 8) (b) (8, 5) (c) (2, 6) (d) (10, 16)
37. 37.In which quadrant does the point (8, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
38. 38.What is the midpoint of the line joining (3, 6) and (13, 2)? (a) (4, 8) (b) (8, 4) (c) (5, 2) (d) (16, 8)
39. 39.What is the distance between the points (7, 9) and (15, 24)? (a) 289 (b) 17 (c) 18 (d) 23
40. 40.In which quadrant does the point (1, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant

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