Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 552 · 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.In which quadrant does the point (−8, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
2. 2.What is the midpoint of the line joining (2, 5) and (12, 17)? (a) (5, 6) (b) (11, 7) (c) (7, 11) (d) (14, 22)
3. 3.What is the distance between the points (2, 14) and (8, 6)? (a) 100 (b) 11 (c) 14 (d) 10
4. 4.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
5. 5.What is the distance between the points (7, 16) and (31, 9)? (a) 31 (b) 26 (c) 625 (d) 25
6. 6.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
7. 7.What is the distance between the points (5, 2) and (13, 17)? (a) 289 (b) 23 (c) 18 (d) 17
8. 8.In which quadrant does the point (3, 8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
9. 9.In which quadrant does the point (−6, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
10. 10.What is the midpoint of the line joining (2, 2) and (12, 4)? (a) (5, 1) (b) (7, 3) (c) (14, 6) (d) (3, 7)
11. 11.In which quadrant does the point (5, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
12. 12.What is the distance between the points (7, 13) and (12, 1)? (a) 17 (b) 14 (c) 13 (d) 169
13. 13.In which quadrant does the point (6, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
14. 14.What is the distance between the points (7, 0) and (19, 16)? (a) 20 (b) 400 (c) 28 (d) 21
15. 15.What is the distance between the points (1, 7) and (6, 19)? (a) 169 (b) 17 (c) 14 (d) 13
16. 16.In which quadrant does the point (−2, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
17. 17.What is the midpoint of the line joining (9, 8) and (11, 16)? (a) (20, 24) (b) (10, 12) (c) (12, 10) (d) (1, 4)
18. 18.In which quadrant does the point (3, −2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
19. 19.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
20. 20.What is the distance between the points (4, 1) and (9, 13)? (a) 169 (b) 13 (c) 17 (d) 14
21. 21.What is the midpoint of the line joining (7, 12) and (9, 4)? (a) (8, 8) (b) (16, 16) (c) (1, 4) (d) (9, 8)
22. 22.What is the distance between the points (0, 1) and (6, 9)? (a) 100 (b) 14 (c) 10 (d) 11
23. 23.In which quadrant does the point (−3, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
24. 24.In which quadrant does the point (8, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
25. 25.What is the midpoint of the line joining (6, 14) and (12, 8)? (a) (18, 22) (b) (11, 9) (c) (3, 3) (d) (9, 11)
26. 26.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
27. 27.What is the distance between the points (7, 6) and (16, 18)? (a) 21 (b) 16 (c) 15 (d) 225
28. 28.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
29. 29.What is the distance between the points (6, 33) and (13, 9)? (a) 31 (b) 625 (c) 25 (d) 26
30. 30.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
31. 31.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
32. 32.In which quadrant does the point (−7, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
33. 33.In which quadrant does the point (1, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
34. 34.In which quadrant does the point (1, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
35. 35.In which quadrant does the point (9, −3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
36. 36.What is the distance between the points (2, 0) and (17, 8)? (a) 289 (b) 23 (c) 17 (d) 18
37. 37.What is the midpoint of the line joining (6, 5) and (14, 9)? (a) (20, 14) (b) (10, 7) (c) (7, 10) (d) (4, 2)
38. 38.What is the midpoint of the line joining (2, 0) and (10, 6)? (a) (3, 6) (b) (4, 3) (c) (6, 3) (d) (12, 6)
39. 39.What is the distance between the points (0, 4) and (3, 0)? (a) 7 (b) 6 (c) 25 (d) 5
40. 40.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100

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