Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 869 · 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 (1, 6) and (4, 10)? (a) 25 (b) 7 (c) 6 (d) 5
2. 2.In which quadrant does the point (2, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
3. 3.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
4. 4.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
5. 5.In which quadrant does the point (−2, −6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
6. 6.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
7. 7.In which quadrant does the point (1, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
8. 8.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
9. 9.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
10. 10.What is the distance between the points (7, 21) and (16, 9)? (a) 15 (b) 21 (c) 225 (d) 16
11. 11.In which quadrant does the point (−4, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
12. 12.What is the midpoint of the line joining (7, 8) and (19, 14)? (a) (26, 22) (b) (13, 11) (c) (6, 3) (d) (11, 13)
13. 13.In which quadrant does the point (−3, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
14. 14.In which quadrant does the point (6, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
15. 15.In which quadrant does the point (−4, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
16. 16.What is the midpoint of the line joining (3, 0) and (13, 6)? (a) (3, 8) (b) (5, 3) (c) (8, 3) (d) (16, 6)
17. 17.What is the distance between the points (1, 12) and (7, 4)? (a) 10 (b) 14 (c) 100 (d) 11
18. 18.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
19. 19.In which quadrant does the point (−5, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
20. 20.In which quadrant does the point (9, −7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
21. 21.In which quadrant does the point (2, −9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
22. 22.What is the distance between the points (5, 12) and (20, 4)? (a) 289 (b) 17 (c) 18 (d) 23
23. 23.In which quadrant does the point (3, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
24. 24.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
25. 25.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
26. 26.In which quadrant does the point (−5, −6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
27. 27.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
28. 28.What is the distance between the points (2, 9) and (5, 5)? (a) 7 (b) 25 (c) 6 (d) 5
29. 29.In which quadrant does the point (3, 9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
30. 30.In which quadrant does the point (2, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
31. 31.What is the midpoint of the line joining (10, 0) and (22, 4)? (a) (32, 4) (b) (2, 16) (c) (6, 2) (d) (16, 2)
32. 32.What is the distance between the points (8, 6) and (23, 14)? (a) 18 (b) 289 (c) 17 (d) 23
33. 33.What is the distance between the points (1, 1) and (25, 8)? (a) 25 (b) 26 (c) 625 (d) 31
34. 34.What is the midpoint of the line joining (2, 3) and (8, 5)? (a) (3, 1) (b) (10, 8) (c) (4, 5) (d) (5, 4)
35. 35.What is the distance between the points (2, 14) and (18, 2)? (a) 20 (b) 400 (c) 21 (d) 28
36. 36.What is the distance between the points (8, 8) and (16, 2)? (a) 100 (b) 11 (c) 14 (d) 10
37. 37.What is the midpoint of the line joining (0, 17) and (12, 9)? (a) (13, 6) (b) (6, 4) (c) (6, 13) (d) (12, 26)
38. 38.What is the midpoint of the line joining (7, 0) and (17, 8)? (a) (12, 4) (b) (4, 12) (c) (5, 4) (d) (24, 8)
39. 39.In which quadrant does the point (4, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
40. 40.In which quadrant does the point (5, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant

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