Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 54 · 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 (3, 4) and (11, 19)? (a) 23 (b) 18 (c) 17 (d) 289
2. 2.What is the distance between the points (3, 0) and (11, 15)? (a) 289 (b) 17 (c) 23 (d) 18
3. 3.What is the distance between the points (9, 3) and (17, 9)? (a) 100 (b) 11 (c) 10 (d) 14
4. 4.What is the midpoint of the line joining (10, 1) and (12, 3)? (a) (1, 1) (b) (11, 2) (c) (2, 11) (d) (22, 4)
5. 5.In which quadrant does the point (−3, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
6. 6.In which quadrant does the point (8, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
7. 7.What is the distance between the points (8, 6) and (14, 14)? (a) 100 (b) 14 (c) 10 (d) 11
8. 8.What is the distance between the points (2, 6) and (10, 0)? (a) 14 (b) 10 (c) 11 (d) 100
9. 9.What is the distance between the points (8, 6) and (20, 15)? (a) 15 (b) 16 (c) 21 (d) 225
10. 10.What is the midpoint of the line joining (10, 4) and (16, 8)? (a) (26, 12) (b) (13, 6) (c) (3, 2) (d) (6, 13)
11. 11.What is the midpoint of the line joining (6, 6) and (10, 18)? (a) (8, 12) (b) (16, 24) (c) (12, 8) (d) (2, 6)
12. 12.In which quadrant does the point (−6, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
13. 13.What is the distance between the points (3, 7) and (12, 19)? (a) 225 (b) 15 (c) 21 (d) 16
14. 14.What is the midpoint of the line joining (5, 4) and (7, 2)? (a) (12, 6) (b) (3, 6) (c) (6, 3) (d) (1, 1)
15. 15.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
16. 16.What is the midpoint of the line joining (1, 14) and (7, 10)? (a) (3, 2) (b) (8, 24) (c) (4, 12) (d) (12, 4)
17. 17.What is the distance between the points (3, 9) and (15, 4)? (a) 14 (b) 169 (c) 17 (d) 13
18. 18.What is the distance between the points (1, 16) and (7, 8)? (a) 10 (b) 14 (c) 100 (d) 11
19. 19.What is the midpoint of the line joining (6, 14) and (18, 2)? (a) (6, 6) (b) (12, 8) (c) (8, 12) (d) (24, 16)
20. 20.What is the distance between the points (8, 9) and (23, 1)? (a) 289 (b) 18 (c) 23 (d) 17
21. 21.In which quadrant does the point (3, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
22. 22.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
23. 23.In which quadrant does the point (−6, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
24. 24.What is the midpoint of the line joining (10, 6) and (18, 18)? (a) (4, 6) (b) (14, 12) (c) (12, 14) (d) (28, 24)
25. 25.What is the midpoint of the line joining (5, 2) and (17, 14)? (a) (22, 16) (b) (11, 8) (c) (6, 6) (d) (8, 11)
26. 26.What is the distance between the points (1, 2) and (6, 14)? (a) 169 (b) 13 (c) 14 (d) 17
27. 27.In which quadrant does the point (3, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
28. 28.In which quadrant does the point (−2, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
29. 29.What is the distance between the points (1, 1) and (8, 25)? (a) 26 (b) 625 (c) 25 (d) 31
30. 30.What is the midpoint of the line joining (1, 13) and (11, 5)? (a) (12, 18) (b) (9, 6) (c) (5, 4) (d) (6, 9)
31. 31.What is the midpoint of the line joining (5, 15) and (7, 5)? (a) (10, 6) (b) (6, 10) (c) (12, 20) (d) (1, 5)
32. 32.What is the distance between the points (3, 2) and (12, 14)? (a) 16 (b) 225 (c) 21 (d) 15
33. 33.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
34. 34.In which quadrant does the point (−9, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
35. 35.What is the distance between the points (0, 11) and (24, 4)? (a) 31 (b) 25 (c) 26 (d) 625
36. 36.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
37. 37.What is the distance between the points (8, 7) and (32, 14)? (a) 625 (b) 31 (c) 26 (d) 25
38. 38.What is the midpoint of the line joining (8, 4) and (16, 10)? (a) (12, 7) (b) (24, 14) (c) (7, 12) (d) (4, 3)
39. 39.What is the distance between the points (3, 8) and (19, 20)? (a) 28 (b) 400 (c) 21 (d) 20
40. 40.In which quadrant does the point (9, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant

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