Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 935 · 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 midpoint of the line joining (10, 6) and (20, 8)? (a) (30, 14) (b) (7, 15) (c) (5, 1) (d) (15, 7)
2. 2.What is the midpoint of the line joining (1, 3) and (5, 7)? (a) (3, 5) (b) (2, 2) (c) (6, 10) (d) (5, 3)
3. 3.What is the distance between the points (4, 0) and (16, 5)? (a) 13 (b) 17 (c) 169 (d) 14
4. 4.What is the distance between the points (2, 9) and (5, 13)? (a) 6 (b) 7 (c) 5 (d) 25
5. 5.What is the distance between the points (0, 18) and (8, 3)? (a) 23 (b) 289 (c) 17 (d) 18
6. 6.What is the distance between the points (5, 3) and (13, 18)? (a) 23 (b) 289 (c) 17 (d) 18
7. 7.In which quadrant does the point (4, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
8. 8.In which quadrant does the point (2, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
9. 9.In which quadrant does the point (−2, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
10. 10.What is the distance between the points (0, 12) and (3, 8)? (a) 6 (b) 7 (c) 5 (d) 25
11. 11.What is the distance between the points (2, 2) and (14, 7)? (a) 13 (b) 14 (c) 169 (d) 17
12. 12.What is the distance between the points (1, 8) and (4, 12)? (a) 6 (b) 7 (c) 25 (d) 5
13. 13.In which quadrant does the point (−2, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
14. 14.What is the distance between the points (6, 8) and (18, 3)? (a) 13 (b) 169 (c) 17 (d) 14
15. 15.What is the distance between the points (9, 2) and (14, 14)? (a) 169 (b) 14 (c) 13 (d) 17
16. 16.What is the distance between the points (7, 15) and (13, 7)? (a) 14 (b) 100 (c) 11 (d) 10
17. 17.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
18. 18.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
19. 19.What is the distance between the points (8, 7) and (20, 23)? (a) 20 (b) 21 (c) 28 (d) 400
20. 20.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
21. 21.What is the distance between the points (1, 8) and (5, 11)? (a) 7 (b) 6 (c) 25 (d) 5
22. 22.In which quadrant does the point (4, 7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
23. 23.What is the distance between the points (8, 5) and (23, 13)? (a) 23 (b) 17 (c) 289 (d) 18
24. 24.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
25. 25.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
26. 26.What is the distance between the points (6, 2) and (12, 10)? (a) 10 (b) 14 (c) 11 (d) 100
27. 27.What is the midpoint of the line joining (10, 2) and (16, 8)? (a) (3, 3) (b) (26, 10) (c) (5, 13) (d) (13, 5)
28. 28.In which quadrant does the point (4, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
29. 29.What is the distance between the points (0, 6) and (16, 18)? (a) 400 (b) 21 (c) 20 (d) 28
30. 30.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
31. 31.In which quadrant does the point (4, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
32. 32.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
33. 33.In which quadrant does the point (8, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
34. 34.What is the distance between the points (5, 4) and (8, 8)? (a) 6 (b) 7 (c) 25 (d) 5
35. 35.What is the midpoint of the line joining (9, 11) and (19, 5)? (a) (28, 16) (b) (8, 14) (c) (14, 8) (d) (5, 3)
36. 36.In which quadrant does the point (−7, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
37. 37.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
38. 38.In which quadrant does the point (−2, −7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
39. 39.What is the distance between the points (1, 6) and (13, 1)? (a) 17 (b) 14 (c) 169 (d) 13
40. 40.In which quadrant does the point (−4, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant

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