Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 831 · 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 (9, 4) and (15, 12)? (a) 100 (b) 10 (c) 14 (d) 11
2. 2.What is the midpoint of the line joining (2, 14) and (10, 10)? (a) (12, 24) (b) (6, 12) (c) (12, 6) (d) (4, 2)
3. 3.In which quadrant does the point (−6, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
4. 4.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
5. 5.What is the distance between the points (5, 1) and (12, 25)? (a) 25 (b) 625 (c) 31 (d) 26
6. 6.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
7. 7.What is the midpoint of the line joining (8, 17) and (16, 5)? (a) (4, 6) (b) (24, 22) (c) (12, 11) (d) (11, 12)
8. 8.What is the distance between the points (1, 14) and (9, 8)? (a) 100 (b) 11 (c) 14 (d) 10
9. 9.What is the midpoint of the line joining (0, 7) and (4, 1)? (a) (2, 3) (b) (2, 4) (c) (4, 2) (d) (4, 8)
10. 10.What is the midpoint of the line joining (10, 9) and (18, 1)? (a) (28, 10) (b) (5, 14) (c) (4, 4) (d) (14, 5)
11. 11.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
12. 12.In which quadrant does the point (−8, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
13. 13.What is the midpoint of the line joining (5, 2) and (11, 12)? (a) (8, 7) (b) (16, 14) (c) (7, 8) (d) (3, 5)
14. 14.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
15. 15.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
16. 16.What is the distance between the points (1, 2) and (10, 14)? (a) 225 (b) 21 (c) 15 (d) 16
17. 17.In which quadrant does the point (7, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
18. 18.In which quadrant does the point (−9, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
19. 19.In which quadrant does the point (4, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
20. 20.In which quadrant does the point (−3, −8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
21. 21.What is the distance between the points (4, 8) and (9, 20)? (a) 14 (b) 169 (c) 17 (d) 13
22. 22.In which quadrant does the point (7, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
23. 23.What is the midpoint of the line joining (7, 8) and (13, 16)? (a) (10, 12) (b) (3, 4) (c) (20, 24) (d) (12, 10)
24. 24.What is the distance between the points (6, 11) and (18, 6)? (a) 17 (b) 169 (c) 14 (d) 13
25. 25.What is the distance between the points (3, 0) and (12, 12)? (a) 225 (b) 21 (c) 15 (d) 16
26. 26.What is the midpoint of the line joining (5, 4) and (17, 6)? (a) (11, 5) (b) (6, 1) (c) (22, 10) (d) (5, 11)
27. 27.What is the midpoint of the line joining (4, 15) and (12, 9)? (a) (12, 8) (b) (8, 12) (c) (16, 24) (d) (4, 3)
28. 28.What is the distance between the points (0, 21) and (12, 5)? (a) 400 (b) 21 (c) 20 (d) 28
29. 29.What is the distance between the points (1, 0) and (4, 4)? (a) 5 (b) 25 (c) 6 (d) 7
30. 30.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
31. 31.In which quadrant does the point (2, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
32. 32.In which quadrant does the point (7, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
33. 33.What is the midpoint of the line joining (0, 17) and (6, 7)? (a) (12, 3) (b) (6, 24) (c) (3, 12) (d) (3, 5)
34. 34.In which quadrant does the point (9, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
35. 35.What is the distance between the points (3, 8) and (15, 13)? (a) 169 (b) 13 (c) 17 (d) 14
36. 36.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
37. 37.What is the midpoint of the line joining (10, 7) and (22, 15)? (a) (16, 11) (b) (32, 22) (c) (11, 16) (d) (6, 4)
38. 38.What is the distance between the points (3, 20) and (15, 4)? (a) 400 (b) 20 (c) 21 (d) 28
39. 39.What is the midpoint of the line joining (1, 7) and (13, 17)? (a) (12, 7) (b) (6, 5) (c) (7, 12) (d) (14, 24)
40. 40.What is the distance between the points (6, 0) and (11, 12)? (a) 13 (b) 17 (c) 14 (d) 169

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