Coordinate Geometry Worksheet for Maths Olympiad

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

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