Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 613 · 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, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
2. 2.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
3. 3.What is the midpoint of the line joining (4, 9) and (16, 1)? (a) (10, 5) (b) (20, 10) (c) (6, 4) (d) (5, 10)
4. 4.In which quadrant does the point (−3, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
5. 5.What is the midpoint of the line joining (10, 4) and (22, 6)? (a) (5, 16) (b) (16, 5) (c) (32, 10) (d) (6, 1)
6. 6.In which quadrant does the point (−1, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
7. 7.What is the distance between the points (8, 18) and (20, 2)? (a) 28 (b) 400 (c) 21 (d) 20
8. 8.In which quadrant does the point (1, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
9. 9.In which quadrant does the point (5, −7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
10. 10.In which quadrant does the point (−1, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
11. 11.What is the midpoint of the line joining (1, 6) and (7, 18)? (a) (4, 12) (b) (3, 6) (c) (12, 4) (d) (8, 24)
12. 12.What is the distance between the points (9, 2) and (21, 11)? (a) 16 (b) 15 (c) 21 (d) 225
13. 13.What is the distance between the points (6, 1) and (30, 8)? (a) 625 (b) 25 (c) 31 (d) 26
14. 14.In which quadrant does the point (−6, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
15. 15.What is the distance between the points (1, 19) and (10, 7)? (a) 21 (b) 15 (c) 16 (d) 225
16. 16.What is the distance between the points (3, 1) and (18, 9)? (a) 18 (b) 23 (c) 289 (d) 17
17. 17.In which quadrant does the point (1, −6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
18. 18.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
19. 19.What is the distance between the points (5, 1) and (13, 16)? (a) 23 (b) 289 (c) 17 (d) 18
20. 20.In which quadrant does the point (−7, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
21. 21.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
22. 22.In which quadrant does the point (2, −4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
23. 23.In which quadrant does the point (−7, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
24. 24.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
25. 25.What is the midpoint of the line joining (7, 10) and (17, 14)? (a) (5, 2) (b) (24, 24) (c) (13, 12) (d) (12, 12)
26. 26.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
27. 27.In which quadrant does the point (9, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
28. 28.What is the distance between the points (2, 6) and (14, 1)? (a) 17 (b) 169 (c) 14 (d) 13
29. 29.In which quadrant does the point (−3, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
30. 30.What is the midpoint of the line joining (9, 5) and (17, 15)? (a) (13, 10) (b) (10, 13) (c) (4, 5) (d) (26, 20)
31. 31.What is the distance between the points (9, 13) and (14, 1)? (a) 14 (b) 17 (c) 13 (d) 169
32. 32.What is the distance between the points (2, 1) and (5, 5)? (a) 25 (b) 5 (c) 7 (d) 6
33. 33.In which quadrant does the point (1, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
34. 34.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
35. 35.What is the distance between the points (3, 2) and (15, 11)? (a) 225 (b) 21 (c) 16 (d) 15
36. 36.What is the distance between the points (5, 7) and (8, 3)? (a) 6 (b) 25 (c) 5 (d) 7
37. 37.What is the midpoint of the line joining (1, 12) and (11, 0)? (a) (6, 6) (b) (5, 6) (c) (12, 12) (d) (7, 6)
38. 38.What is the midpoint of the line joining (4, 20) and (14, 10)? (a) (5, 5) (b) (9, 15) (c) (18, 30) (d) (15, 9)
39. 39.What is the distance between the points (7, 12) and (10, 8)? (a) 5 (b) 6 (c) 7 (d) 25
40. 40.In which quadrant does the point (9, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant

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