Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 232 · 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 (5, 12) and (11, 4)? (a) 100 (b) 14 (c) 10 (d) 11
2. 2.What is the distance between the points (6, 16) and (14, 1)? (a) 23 (b) 18 (c) 17 (d) 289
3. 3.What is the midpoint of the line joining (7, 10) and (11, 18)? (a) (2, 4) (b) (14, 9) (c) (9, 14) (d) (18, 28)
4. 4.What is the distance between the points (0, 17) and (16, 5)? (a) 20 (b) 21 (c) 28 (d) 400
5. 5.What is the midpoint of the line joining (1, 15) and (3, 7)? (a) (11, 2) (b) (1, 4) (c) (2, 11) (d) (4, 22)
6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
7. 7.What is the distance between the points (1, 7) and (13, 12)? (a) 17 (b) 14 (c) 13 (d) 169
8. 8.In which quadrant does the point (−9, −7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
9. 9.In which quadrant does the point (6, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
10. 10.What is the distance between the points (9, 2) and (24, 10)? (a) 17 (b) 18 (c) 23 (d) 289
11. 11.What is the midpoint of the line joining (1, 6) and (3, 0)? (a) (2, 3) (b) (4, 6) (c) (1, 3) (d) (3, 2)
12. 12.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
13. 13.In which quadrant does the point (−9, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
14. 14.What is the distance between the points (9, 2) and (17, 17)? (a) 23 (b) 289 (c) 17 (d) 18
15. 15.What is the midpoint of the line joining (9, 7) and (21, 17)? (a) (12, 15) (b) (30, 24) (c) (15, 12) (d) (6, 5)
16. 16.What is the distance between the points (0, 7) and (12, 23)? (a) 21 (b) 20 (c) 28 (d) 400
17. 17.What is the distance between the points (9, 5) and (14, 17)? (a) 169 (b) 14 (c) 17 (d) 13
18. 18.What is the distance between the points (8, 0) and (20, 5)? (a) 17 (b) 13 (c) 14 (d) 169
19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
20. 20.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
21. 21.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
22. 22.In which quadrant does the point (−3, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
23. 23.What is the distance between the points (2, 7) and (5, 11)? (a) 5 (b) 7 (c) 6 (d) 25
24. 24.In which quadrant does the point (7, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
25. 25.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
26. 26.What is the midpoint of the line joining (1, 14) and (5, 8)? (a) (6, 22) (b) (2, 3) (c) (11, 3) (d) (3, 11)
27. 27.What is the distance between the points (1, 2) and (17, 14)? (a) 28 (b) 20 (c) 21 (d) 400
28. 28.In which quadrant does the point (−1, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
29. 29.In which quadrant does the point (3, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
30. 30.In which quadrant does the point (2, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
31. 31.What is the distance between the points (6, 1) and (14, 7)? (a) 14 (b) 10 (c) 100 (d) 11
32. 32.In which quadrant does the point (9, −2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
33. 33.In which quadrant does the point (3, 6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
34. 34.What is the midpoint of the line joining (9, 14) and (15, 8)? (a) (3, 3) (b) (12, 11) (c) (11, 12) (d) (24, 22)
35. 35.What is the midpoint of the line joining (2, 8) and (6, 6)? (a) (8, 14) (b) (4, 7) (c) (2, 1) (d) (7, 4)
36. 36.What is the distance between the points (2, 12) and (11, 0)? (a) 16 (b) 225 (c) 15 (d) 21
37. 37.In which quadrant does the point (1, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
38. 38.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
39. 39.In which quadrant does the point (−9, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
40. 40.What is the midpoint of the line joining (3, 8) and (9, 18)? (a) (12, 26) (b) (13, 6) (c) (6, 13) (d) (3, 5)

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