Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 200 · 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, 9) and (23, 17)? (a) 289 (b) 17 (c) 18 (d) 23
2. 2.What is the distance between the points (8, 15) and (16, 9)? (a) 10 (b) 100 (c) 14 (d) 11
3. 3.What is the midpoint of the line joining (3, 6) and (7, 18)? (a) (5, 12) (b) (10, 24) (c) (12, 5) (d) (2, 6)
4. 4.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 289 (d) 23
5. 5.What is the midpoint of the line joining (9, 6) and (19, 14)? (a) (28, 20) (b) (10, 14) (c) (5, 4) (d) (14, 10)
6. 6.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
7. 7.In which quadrant does the point (2, −1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
8. 8.In which quadrant does the point (−8, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
9. 9.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
10. 10.What is the distance between the points (2, 8) and (7, 20)? (a) 13 (b) 17 (c) 14 (d) 169
11. 11.What is the distance between the points (3, 9) and (9, 1)? (a) 11 (b) 100 (c) 14 (d) 10
12. 12.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
13. 13.What is the midpoint of the line joining (1, 4) and (11, 10)? (a) (12, 14) (b) (6, 7) (c) (7, 6) (d) (5, 3)
14. 14.What is the distance between the points (4, 4) and (16, 20)? (a) 28 (b) 400 (c) 20 (d) 21
15. 15.What is the midpoint of the line joining (10, 1) and (18, 7)? (a) (4, 3) (b) (14, 4) (c) (4, 14) (d) (28, 8)
16. 16.What is the distance between the points (8, 2) and (15, 26)? (a) 25 (b) 26 (c) 31 (d) 625
17. 17.What is the midpoint of the line joining (5, 4) and (11, 2)? (a) (16, 6) (b) (8, 3) (c) (3, 8) (d) (3, 1)
18. 18.What is the midpoint of the line joining (1, 10) and (5, 2)? (a) (6, 12) (b) (6, 3) (c) (2, 4) (d) (3, 6)
19. 19.What is the midpoint of the line joining (2, 5) and (10, 3)? (a) (12, 8) (b) (6, 4) (c) (4, 6) (d) (4, 1)
20. 20.What is the distance between the points (1, 3) and (4, 7)? (a) 7 (b) 6 (c) 5 (d) 25
21. 21.What is the distance between the points (9, 9) and (25, 21)? (a) 400 (b) 21 (c) 20 (d) 28
22. 22.What is the midpoint of the line joining (1, 3) and (13, 5)? (a) (14, 8) (b) (6, 1) (c) (7, 4) (d) (4, 7)
23. 23.What is the midpoint of the line joining (0, 8) and (2, 16)? (a) (1, 4) (b) (2, 24) (c) (1, 12) (d) (12, 1)
24. 24.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
25. 25.What is the distance between the points (8, 14) and (24, 2)? (a) 28 (b) 400 (c) 21 (d) 20
26. 26.What is the distance between the points (9, 5) and (21, 10)? (a) 14 (b) 13 (c) 169 (d) 17
27. 27.In which quadrant does the point (2, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
28. 28.In which quadrant does the point (1, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
29. 29.What is the distance between the points (5, 7) and (13, 1)? (a) 100 (b) 14 (c) 10 (d) 11
30. 30.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
31. 31.What is the distance between the points (2, 6) and (17, 14)? (a) 17 (b) 18 (c) 23 (d) 289
32. 32.In which quadrant does the point (3, −7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
33. 33.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
34. 34.What is the distance between the points (3, 4) and (11, 19)? (a) 289 (b) 23 (c) 17 (d) 18
35. 35.What is the distance between the points (6, 28) and (13, 4)? (a) 25 (b) 26 (c) 31 (d) 625
36. 36.What is the midpoint of the line joining (5, 2) and (7, 10)? (a) (6, 6) (b) (12, 12) (c) (1, 4) (d) (7, 6)
37. 37.In which quadrant does the point (2, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
38. 38.What is the distance between the points (4, 8) and (12, 23)? (a) 17 (b) 18 (c) 23 (d) 289
39. 39.What is the distance between the points (1, 2) and (4, 6)? (a) 5 (b) 7 (c) 6 (d) 25
40. 40.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5

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