Coordinate Geometry Worksheet for Maths Olympiad

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

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