Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 581 · 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 (8, 24) and (20, 8)? (a) 400 (b) 28 (c) 20 (d) 21
2. 2.What is the midpoint of the line joining (2, 5) and (8, 3)? (a) (4, 5) (b) (10, 8) (c) (5, 4) (d) (3, 1)
3. 3.In which quadrant does the point (−2, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
4. 4.In which quadrant does the point (−2, −4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
5. 5.What is the midpoint of the line joining (2, 16) and (14, 8)? (a) (16, 24) (b) (12, 8) (c) (6, 4) (d) (8, 12)
6. 6.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
7. 7.What is the distance between the points (0, 0) and (5, 12)? (a) 17 (b) 13 (c) 14 (d) 169
8. 8.In which quadrant does the point (3, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
9. 9.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
10. 10.What is the distance between the points (7, 10) and (15, 4)? (a) 10 (b) 11 (c) 100 (d) 14
11. 11.What is the distance between the points (3, 3) and (15, 12)? (a) 16 (b) 21 (c) 15 (d) 225
12. 12.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
13. 13.What is the distance between the points (1, 15) and (10, 3)? (a) 225 (b) 21 (c) 16 (d) 15
14. 14.What is the distance between the points (9, 9) and (21, 25)? (a) 28 (b) 20 (c) 21 (d) 400
15. 15.In which quadrant does the point (−5, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
16. 16.In which quadrant does the point (−5, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
17. 17.What is the distance between the points (8, 9) and (14, 17)? (a) 11 (b) 10 (c) 100 (d) 14
18. 18.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
19. 19.What is the midpoint of the line joining (8, 8) and (14, 12)? (a) (3, 2) (b) (10, 11) (c) (11, 10) (d) (22, 20)
20. 20.What is the midpoint of the line joining (6, 21) and (14, 9)? (a) (10, 15) (b) (15, 10) (c) (4, 6) (d) (20, 30)
21. 21.In which quadrant does the point (−3, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
22. 22.What is the midpoint of the line joining (4, 0) and (6, 6)? (a) (1, 3) (b) (3, 5) (c) (5, 3) (d) (10, 6)
23. 23.What is the distance between the points (1, 13) and (6, 1)? (a) 14 (b) 169 (c) 17 (d) 13
24. 24.In which quadrant does the point (1, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
25. 25.What is the midpoint of the line joining (2, 4) and (6, 2)? (a) (3, 4) (b) (2, 1) (c) (4, 3) (d) (8, 6)
26. 26.What is the distance between the points (5, 8) and (13, 14)? (a) 100 (b) 11 (c) 10 (d) 14
27. 27.In which quadrant does the point (4, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
28. 28.In which quadrant does the point (−2, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
29. 29.What is the distance between the points (1, 12) and (5, 9)? (a) 5 (b) 6 (c) 7 (d) 25
30. 30.What is the midpoint of the line joining (3, 14) and (15, 2)? (a) (18, 16) (b) (6, 6) (c) (9, 8) (d) (8, 9)
31. 31.In which quadrant does the point (−1, 7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
32. 32.What is the midpoint of the line joining (0, 15) and (12, 9)? (a) (12, 24) (b) (6, 3) (c) (12, 6) (d) (6, 12)
33. 33.What is the distance between the points (7, 13) and (10, 9)? (a) 6 (b) 7 (c) 25 (d) 5
34. 34.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
35. 35.What is the midpoint of the line joining (2, 5) and (6, 3)? (a) (5, 4) (b) (4, 4) (c) (2, 1) (d) (8, 8)
36. 36.In which quadrant does the point (−2, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
37. 37.What is the distance between the points (1, 8) and (25, 1)? (a) 26 (b) 625 (c) 31 (d) 25
38. 38.In which quadrant does the point (6, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
39. 39.What is the distance between the points (2, 25) and (9, 1)? (a) 25 (b) 625 (c) 31 (d) 26
40. 40.What is the distance between the points (0, 0) and (4, 3)? (a) 6 (b) 25 (c) 7 (d) 5

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