Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 107 · 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, 7) and (16, 1)? (a) (12, 4) (b) (4, 12) (c) (4, 3) (d) (24, 8)
2. 2.What is the midpoint of the line joining (5, 7) and (7, 1)? (a) (4, 6) (b) (1, 3) (c) (12, 8) (d) (6, 4)
3. 3.In which quadrant does the point (−1, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
4. 4.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
5. 5.What is the distance between the points (3, 1) and (15, 10)? (a) 21 (b) 225 (c) 15 (d) 16
6. 6.What is the distance between the points (5, 6) and (17, 15)? (a) 16 (b) 225 (c) 21 (d) 15
7. 7.What is the distance between the points (2, 21) and (7, 9)? (a) 13 (b) 17 (c) 169 (d) 14
8. 8.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
9. 9.In which quadrant does the point (−9, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
10. 10.In which quadrant does the point (−4, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
11. 11.In which quadrant does the point (5, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
12. 12.What is the distance between the points (7, 10) and (11, 7)? (a) 6 (b) 7 (c) 25 (d) 5
13. 13.In which quadrant does the point (8, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
14. 14.What is the distance between the points (1, 20) and (6, 8)? (a) 14 (b) 13 (c) 17 (d) 169
15. 15.What is the distance between the points (0, 13) and (6, 5)? (a) 10 (b) 14 (c) 100 (d) 11
16. 16.In which quadrant does the point (−3, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
17. 17.In which quadrant does the point (5, 4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
18. 18.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
19. 19.In which quadrant does the point (−7, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
20. 20.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
21. 21.In which quadrant does the point (2, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
22. 22.What is the midpoint of the line joining (0, 5) and (12, 11)? (a) (6, 3) (b) (8, 6) (c) (6, 8) (d) (12, 16)
23. 23.What is the distance between the points (1, 9) and (7, 1)? (a) 11 (b) 100 (c) 14 (d) 10
24. 24.What is the distance between the points (6, 18) and (11, 6)? (a) 14 (b) 13 (c) 169 (d) 17
25. 25.In which quadrant does the point (1, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
26. 26.What is the midpoint of the line joining (0, 11) and (12, 5)? (a) (6, 8) (b) (12, 16) (c) (8, 6) (d) (6, 3)
27. 27.What is the midpoint of the line joining (1, 10) and (3, 6)? (a) (2, 8) (b) (8, 2) (c) (1, 2) (d) (4, 16)
28. 28.What is the midpoint of the line joining (2, 7) and (10, 19)? (a) (13, 6) (b) (6, 13) (c) (12, 26) (d) (4, 6)
29. 29.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
30. 30.In which quadrant does the point (2, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
31. 31.What is the midpoint of the line joining (8, 0) and (16, 8)? (a) (24, 8) (b) (4, 12) (c) (12, 4) (d) (4, 4)
32. 32.What is the distance between the points (7, 8) and (31, 1)? (a) 25 (b) 31 (c) 26 (d) 625
33. 33.What is the distance between the points (1, 5) and (10, 17)? (a) 15 (b) 16 (c) 225 (d) 21
34. 34.What is the distance between the points (3, 4) and (27, 11)? (a) 25 (b) 625 (c) 31 (d) 26
35. 35.In which quadrant does the point (−4, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
36. 36.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
37. 37.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
38. 38.What is the midpoint of the line joining (6, 3) and (12, 5)? (a) (18, 8) (b) (4, 9) (c) (9, 4) (d) (3, 1)
39. 39.In which quadrant does the point (8, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
40. 40.What is the distance between the points (2, 8) and (9, 32)? (a) 625 (b) 26 (c) 25 (d) 31

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