Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 877 · 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 (6, 4) and (21, 12)? (a) 17 (b) 23 (c) 289 (d) 18
2. 2.What is the distance between the points (3, 24) and (10, 0)? (a) 625 (b) 25 (c) 26 (d) 31
3. 3.What is the distance between the points (2, 29) and (9, 5)? (a) 625 (b) 26 (c) 25 (d) 31
4. 4.What is the distance between the points (2, 11) and (26, 4)? (a) 31 (b) 25 (c) 26 (d) 625
5. 5.In which quadrant does the point (−9, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
6. 6.In which quadrant does the point (−9, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
8. 8.What is the distance between the points (7, 0) and (14, 24)? (a) 26 (b) 625 (c) 25 (d) 31
9. 9.In which quadrant does the point (−4, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
10. 10.What is the midpoint of the line joining (6, 10) and (8, 6)? (a) (1, 2) (b) (7, 8) (c) (8, 7) (d) (14, 16)
11. 11.In which quadrant does the point (2, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
12. 12.What is the distance between the points (5, 4) and (9, 7)? (a) 25 (b) 7 (c) 6 (d) 5
13. 13.What is the midpoint of the line joining (0, 6) and (12, 16)? (a) (11, 6) (b) (12, 22) (c) (6, 5) (d) (6, 11)
14. 14.What is the distance between the points (0, 2) and (5, 14)? (a) 17 (b) 13 (c) 14 (d) 169
15. 15.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
16. 16.What is the midpoint of the line joining (8, 2) and (12, 8)? (a) (5, 10) (b) (20, 10) (c) (2, 3) (d) (10, 5)
17. 17.What is the distance between the points (3, 12) and (15, 3)? (a) 15 (b) 21 (c) 225 (d) 16
18. 18.What is the distance between the points (6, 10) and (14, 4)? (a) 14 (b) 100 (c) 11 (d) 10
19. 19.What is the midpoint of the line joining (3, 16) and (7, 8)? (a) (10, 24) (b) (5, 12) (c) (2, 4) (d) (12, 5)
20. 20.What is the distance between the points (9, 9) and (21, 0)? (a) 15 (b) 225 (c) 21 (d) 16
21. 21.What is the distance between the points (9, 3) and (12, 7)? (a) 7 (b) 6 (c) 25 (d) 5
22. 22.What is the midpoint of the line joining (1, 10) and (5, 0)? (a) (5, 3) (b) (3, 5) (c) (2, 5) (d) (6, 10)
23. 23.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
24. 24.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
25. 25.In which quadrant does the point (8, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
26. 26.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
27. 27.What is the distance between the points (4, 4) and (19, 12)? (a) 17 (b) 289 (c) 18 (d) 23
28. 28.What is the midpoint of the line joining (4, 7) and (12, 19)? (a) (4, 6) (b) (13, 8) (c) (8, 13) (d) (16, 26)
29. 29.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
30. 30.What is the distance between the points (5, 2) and (8, 6)? (a) 7 (b) 6 (c) 5 (d) 25
31. 31.What is the distance between the points (3, 6) and (27, 13)? (a) 625 (b) 31 (c) 26 (d) 25
32. 32.What is the distance between the points (2, 8) and (9, 32)? (a) 31 (b) 625 (c) 25 (d) 26
33. 33.What is the midpoint of the line joining (4, 5) and (12, 17)? (a) (11, 8) (b) (8, 11) (c) (16, 22) (d) (4, 6)
34. 34.What is the midpoint of the line joining (4, 4) and (14, 0)? (a) (18, 4) (b) (2, 9) (c) (9, 2) (d) (5, 2)
35. 35.What is the distance between the points (8, 0) and (20, 9)? (a) 16 (b) 15 (c) 21 (d) 225
36. 36.What is the midpoint of the line joining (7, 5) and (13, 9)? (a) (20, 14) (b) (7, 10) (c) (10, 7) (d) (3, 2)
37. 37.What is the distance between the points (0, 2) and (9, 14)? (a) 16 (b) 21 (c) 15 (d) 225
38. 38.What is the midpoint of the line joining (10, 6) and (12, 4)? (a) (11, 5) (b) (22, 10) (c) (5, 11) (d) (1, 1)
39. 39.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
40. 40.In which quadrant does the point (3, −4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant

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