Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 204 · 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.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
2. 2.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
3. 3.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
4. 4.In which quadrant does the point (4, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
5. 5.In which quadrant does the point (1, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
6. 6.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
7. 7.In which quadrant does the point (3, −8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
8. 8.In which quadrant does the point (8, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
9. 9.What is the midpoint of the line joining (7, 8) and (19, 10)? (a) (13, 9) (b) (6, 1) (c) (26, 18) (d) (9, 13)
10. 10.In which quadrant does the point (−3, −2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
11. 11.What is the distance between the points (8, 22) and (16, 7)? (a) 289 (b) 18 (c) 23 (d) 17
12. 12.What is the distance between the points (7, 13) and (12, 1)? (a) 14 (b) 17 (c) 13 (d) 169
13. 13.What is the distance between the points (4, 8) and (8, 11)? (a) 5 (b) 25 (c) 7 (d) 6
14. 14.What is the distance between the points (9, 12) and (12, 8)? (a) 7 (b) 25 (c) 6 (d) 5
15. 15.What is the distance between the points (5, 8) and (17, 17)? (a) 21 (b) 16 (c) 15 (d) 225
16. 16.What is the distance between the points (7, 9) and (31, 16)? (a) 31 (b) 625 (c) 25 (d) 26
17. 17.What is the midpoint of the line joining (1, 12) and (5, 0)? (a) (6, 12) (b) (3, 6) (c) (6, 3) (d) (2, 6)
18. 18.What is the distance between the points (9, 9) and (24, 17)? (a) 23 (b) 18 (c) 17 (d) 289
19. 19.What is the distance between the points (7, 20) and (12, 8)? (a) 13 (b) 17 (c) 14 (d) 169
20. 20.What is the midpoint of the line joining (4, 1) and (10, 9)? (a) (5, 7) (b) (14, 10) (c) (3, 4) (d) (7, 5)
21. 21.What is the distance between the points (2, 6) and (8, 14)? (a) 100 (b) 14 (c) 11 (d) 10
22. 22.In which quadrant does the point (−7, −7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
23. 23.What is the midpoint of the line joining (2, 10) and (14, 16)? (a) (16, 26) (b) (8, 13) (c) (6, 3) (d) (13, 8)
24. 24.What is the midpoint of the line joining (9, 11) and (13, 9)? (a) (10, 11) (b) (22, 20) (c) (2, 1) (d) (11, 10)
25. 25.What is the distance between the points (0, 6) and (12, 15)? (a) 225 (b) 16 (c) 21 (d) 15
26. 26.What is the distance between the points (2, 9) and (10, 3)? (a) 100 (b) 11 (c) 10 (d) 14
27. 27.What is the distance between the points (9, 5) and (17, 20)? (a) 18 (b) 289 (c) 17 (d) 23
28. 28.In which quadrant does the point (−7, 9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
29. 29.In which quadrant does the point (9, 3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
30. 30.What is the distance between the points (2, 9) and (8, 1)? (a) 14 (b) 11 (c) 100 (d) 10
31. 31.In which quadrant does the point (−9, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
32. 32.What is the midpoint of the line joining (3, 13) and (7, 5)? (a) (10, 18) (b) (5, 9) (c) (9, 5) (d) (2, 4)
33. 33.What is the distance between the points (8, 13) and (20, 8)? (a) 17 (b) 13 (c) 14 (d) 169
34. 34.What is the distance between the points (6, 0) and (12, 8)? (a) 100 (b) 11 (c) 14 (d) 10
35. 35.What is the midpoint of the line joining (6, 2) and (16, 6)? (a) (11, 4) (b) (22, 8) (c) (5, 2) (d) (4, 11)
36. 36.What is the distance between the points (6, 0) and (18, 5)? (a) 14 (b) 17 (c) 169 (d) 13
37. 37.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
38. 38.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
39. 39.What is the midpoint of the line joining (4, 3) and (10, 1)? (a) (2, 7) (b) (14, 4) (c) (7, 2) (d) (3, 1)
40. 40.In which quadrant does the point (3, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant

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