Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 458 · 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 (8, 4) and (10, 6)? (a) (18, 10) (b) (1, 1) (c) (9, 5) (d) (5, 9)
2. 2.What is the distance between the points (5, 4) and (9, 1)? (a) 6 (b) 25 (c) 5 (d) 7
3. 3.In which quadrant does the point (2, 3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
4. 4.What is the midpoint of the line joining (9, 1) and (15, 11)? (a) (24, 12) (b) (6, 12) (c) (3, 5) (d) (12, 6)
5. 5.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
6. 6.What is the distance between the points (5, 5) and (9, 2)? (a) 5 (b) 7 (c) 6 (d) 25
7. 7.In which quadrant does the point (−6, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
8. 8.What is the distance between the points (2, 1) and (10, 16)? (a) 18 (b) 289 (c) 23 (d) 17
9. 9.In which quadrant does the point (7, −8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
10. 10.What is the midpoint of the line joining (0, 4) and (10, 12)? (a) (8, 5) (b) (5, 4) (c) (5, 8) (d) (10, 16)
11. 11.In which quadrant does the point (4, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
12. 12.What is the midpoint of the line joining (8, 6) and (20, 8)? (a) (7, 14) (b) (14, 7) (c) (6, 1) (d) (28, 14)
13. 13.What is the distance between the points (9, 14) and (15, 6)? (a) 11 (b) 100 (c) 10 (d) 14
14. 14.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
15. 15.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
16. 16.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
17. 17.What is the midpoint of the line joining (7, 1) and (15, 9)? (a) (22, 10) (b) (4, 4) (c) (5, 11) (d) (11, 5)
18. 18.In which quadrant does the point (9, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
19. 19.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
20. 20.What is the distance between the points (8, 10) and (14, 2)? (a) 10 (b) 100 (c) 11 (d) 14
21. 21.What is the midpoint of the line joining (3, 12) and (9, 6)? (a) (9, 6) (b) (6, 9) (c) (3, 3) (d) (12, 18)
22. 22.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
23. 23.In which quadrant does the point (7, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
24. 24.What is the midpoint of the line joining (8, 9) and (14, 11)? (a) (10, 11) (b) (11, 10) (c) (22, 20) (d) (3, 1)
25. 25.What is the distance between the points (3, 9) and (11, 15)? (a) 11 (b) 10 (c) 100 (d) 14
26. 26.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
27. 27.What is the distance between the points (6, 15) and (21, 7)? (a) 289 (b) 23 (c) 17 (d) 18
28. 28.What is the distance between the points (5, 14) and (17, 9)? (a) 13 (b) 169 (c) 14 (d) 17
29. 29.What is the distance between the points (2, 0) and (7, 12)? (a) 17 (b) 169 (c) 13 (d) 14
30. 30.What is the midpoint of the line joining (3, 12) and (5, 10)? (a) (8, 22) (b) (1, 1) (c) (4, 11) (d) (11, 4)
31. 31.What is the distance between the points (1, 8) and (13, 17)? (a) 225 (b) 15 (c) 21 (d) 16
32. 32.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
33. 33.In which quadrant does the point (3, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
34. 34.In which quadrant does the point (−6, −4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
35. 35.What is the distance between the points (0, 6) and (6, 14)? (a) 10 (b) 14 (c) 11 (d) 100
36. 36.What is the midpoint of the line joining (8, 3) and (10, 9)? (a) (1, 3) (b) (6, 9) (c) (9, 6) (d) (18, 12)
37. 37.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
38. 38.What is the midpoint of the line joining (5, 19) and (7, 7)? (a) (12, 26) (b) (13, 6) (c) (1, 6) (d) (6, 13)
39. 39.What is the midpoint of the line joining (6, 9) and (16, 7)? (a) (8, 11) (b) (22, 16) (c) (11, 8) (d) (5, 1)
40. 40.What is the distance between the points (9, 5) and (17, 20)? (a) 18 (b) 17 (c) 289 (d) 23

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