Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 102 · 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 (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
2. 2.In which quadrant does the point (6, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
3. 3.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
4. 4.What is the midpoint of the line joining (3, 5) and (7, 15)? (a) (5, 10) (b) (10, 20) (c) (2, 5) (d) (10, 5)
5. 5.What is the midpoint of the line joining (1, 14) and (11, 4)? (a) (5, 5) (b) (6, 9) (c) (12, 18) (d) (9, 6)
6. 6.In which quadrant does the point (−3, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
7. 7.What is the midpoint of the line joining (4, 8) and (8, 4)? (a) (12, 12) (b) (7, 6) (c) (6, 6) (d) (2, 2)
8. 8.What is the midpoint of the line joining (6, 12) and (10, 10)? (a) (16, 22) (b) (8, 11) (c) (11, 8) (d) (2, 1)
9. 9.In which quadrant does the point (1, −8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
10. 10.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
11. 11.In which quadrant does the point (5, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
12. 12.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
13. 13.In which quadrant does the point (4, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
14. 14.In which quadrant does the point (−9, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
15. 15.What is the midpoint of the line joining (9, 15) and (15, 9)? (a) (3, 3) (b) (13, 12) (c) (12, 12) (d) (24, 24)
16. 16.What is the distance between the points (7, 6) and (22, 14)? (a) 18 (b) 17 (c) 289 (d) 23
17. 17.What is the midpoint of the line joining (2, 4) and (4, 8)? (a) (6, 3) (b) (3, 6) (c) (6, 12) (d) (1, 2)
18. 18.In which quadrant does the point (4, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
19. 19.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
20. 20.What is the distance between the points (1, 4) and (13, 20)? (a) 400 (b) 28 (c) 20 (d) 21
21. 21.What is the midpoint of the line joining (6, 18) and (8, 8)? (a) (1, 5) (b) (7, 13) (c) (13, 7) (d) (14, 26)
22. 22.In which quadrant does the point (−9, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
23. 23.What is the midpoint of the line joining (0, 7) and (12, 9)? (a) (6, 1) (b) (6, 8) (c) (8, 6) (d) (12, 16)
24. 24.In which quadrant does the point (3, 4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
25. 25.What is the midpoint of the line joining (1, 10) and (9, 20)? (a) (10, 30) (b) (4, 5) (c) (5, 15) (d) (15, 5)
26. 26.In which quadrant does the point (7, −6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
27. 27.In which quadrant does the point (−7, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
28. 28.What is the distance between the points (6, 4) and (21, 12)? (a) 18 (b) 17 (c) 23 (d) 289
29. 29.What is the distance between the points (4, 25) and (11, 1)? (a) 26 (b) 625 (c) 25 (d) 31
30. 30.In which quadrant does the point (−8, 2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
31. 31.In which quadrant does the point (5, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
32. 32.In which quadrant does the point (8, 2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
33. 33.In which quadrant does the point (−3, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
34. 34.In which quadrant does the point (−6, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
35. 35.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
36. 36.In which quadrant does the point (3, 9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
37. 37.What is the midpoint of the line joining (10, 7) and (14, 3)? (a) (2, 2) (b) (24, 10) (c) (5, 12) (d) (12, 5)
38. 38.What is the distance between the points (1, 8) and (25, 15)? (a) 31 (b) 25 (c) 625 (d) 26
39. 39.In which quadrant does the point (4, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
40. 40.What is the distance between the points (3, 1) and (12, 13)? (a) 16 (b) 15 (c) 21 (d) 225

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