Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 796 · 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 (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
2. 2.In which quadrant does the point (−8, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
3. 3.In which quadrant does the point (6, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
4. 4.In which quadrant does the point (7, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
5. 5.What is the midpoint of the line joining (7, 7) and (13, 3)? (a) (5, 10) (b) (3, 2) (c) (20, 10) (d) (10, 5)
6. 6.In which quadrant does the point (2, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
8. 8.What is the midpoint of the line joining (6, 9) and (10, 21)? (a) (15, 8) (b) (2, 6) (c) (8, 15) (d) (16, 30)
9. 9.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
10. 10.In which quadrant does the point (2, 2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
11. 11.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
12. 12.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
13. 13.In which quadrant does the point (−6, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
14. 14.In which quadrant does the point (−1, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
15. 15.What is the midpoint of the line joining (0, 6) and (6, 0)? (a) (6, 6) (b) (3, 4) (c) (3, 3) (d) (4, 3)
16. 16.In which quadrant does the point (4, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
17. 17.What is the distance between the points (4, 9) and (16, 25)? (a) 400 (b) 20 (c) 21 (d) 28
18. 18.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
19. 19.In which quadrant does the point (8, −4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
20. 20.In which quadrant does the point (−3, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
21. 21.What is the midpoint of the line joining (4, 1) and (10, 5)? (a) (7, 3) (b) (3, 7) (c) (3, 2) (d) (14, 6)
22. 22.What is the distance between the points (9, 4) and (13, 1)? (a) 6 (b) 5 (c) 7 (d) 25
23. 23.What is the distance between the points (5, 9) and (17, 25)? (a) 21 (b) 20 (c) 28 (d) 400
24. 24.What is the midpoint of the line joining (1, 1) and (9, 11)? (a) (10, 12) (b) (4, 5) (c) (5, 6) (d) (6, 5)
25. 25.What is the midpoint of the line joining (10, 10) and (20, 18)? (a) (14, 15) (b) (30, 28) (c) (15, 14) (d) (5, 4)
26. 26.What is the distance between the points (8, 0) and (14, 8)? (a) 11 (b) 10 (c) 14 (d) 100
27. 27.What is the distance between the points (1, 16) and (13, 0)? (a) 20 (b) 400 (c) 21 (d) 28
28. 28.What is the distance between the points (1, 8) and (13, 3)? (a) 17 (b) 14 (c) 169 (d) 13
29. 29.What is the distance between the points (2, 4) and (17, 12)? (a) 289 (b) 23 (c) 18 (d) 17
30. 30.What is the midpoint of the line joining (8, 0) and (12, 4)? (a) (20, 4) (b) (10, 2) (c) (2, 2) (d) (2, 10)
31. 31.In which quadrant does the point (1, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
32. 32.What is the distance between the points (2, 16) and (14, 0)? (a) 400 (b) 20 (c) 21 (d) 28
33. 33.In which quadrant does the point (−2, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
34. 34.In which quadrant does the point (−6, 5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
35. 35.What is the distance between the points (0, 4) and (5, 16)? (a) 17 (b) 13 (c) 169 (d) 14
36. 36.What is the distance between the points (3, 6) and (7, 9)? (a) 7 (b) 25 (c) 6 (d) 5
37. 37.What is the midpoint of the line joining (4, 3) and (6, 9)? (a) (10, 12) (b) (6, 5) (c) (1, 3) (d) (5, 6)
38. 38.What is the distance between the points (4, 12) and (28, 5)? (a) 26 (b) 31 (c) 625 (d) 25
39. 39.In which quadrant does the point (−4, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
40. 40.What is the midpoint of the line joining (0, 5) and (12, 9)? (a) (6, 2) (b) (7, 6) (c) (6, 7) (d) (12, 14)

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