Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 391 · 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 (3, 12) and (13, 0)? (a) (6, 8) (b) (5, 6) (c) (16, 12) (d) (8, 6)
2. 2.In which quadrant does the point (7, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
3. 3.What is the midpoint of the line joining (5, 9) and (11, 13)? (a) (3, 2) (b) (16, 22) (c) (11, 8) (d) (8, 11)
4. 4.What is the distance between the points (4, 15) and (10, 7)? (a) 10 (b) 11 (c) 14 (d) 100
5. 5.In which quadrant does the point (−4, 9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
6. 6.In which quadrant does the point (−9, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
7. 7.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
8. 8.What is the distance between the points (5, 9) and (8, 13)? (a) 7 (b) 5 (c) 25 (d) 6
9. 9.In which quadrant does the point (−3, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
10. 10.In which quadrant does the point (2, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
11. 11.In which quadrant does the point (9, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
12. 12.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
13. 13.What is the distance between the points (2, 7) and (9, 31)? (a) 31 (b) 625 (c) 26 (d) 25
14. 14.What is the distance between the points (9, 0) and (14, 12)? (a) 17 (b) 13 (c) 169 (d) 14
15. 15.What is the midpoint of the line joining (10, 1) and (12, 9)? (a) (1, 4) (b) (11, 5) (c) (5, 11) (d) (22, 10)
16. 16.What is the distance between the points (6, 6) and (14, 21)? (a) 23 (b) 17 (c) 18 (d) 289
17. 17.What is the distance between the points (0, 10) and (6, 2)? (a) 11 (b) 100 (c) 10 (d) 14
18. 18.What is the midpoint of the line joining (3, 7) and (13, 5)? (a) (16, 12) (b) (5, 1) (c) (6, 8) (d) (8, 6)
19. 19.In which quadrant does the point (−4, −3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
20. 20.What is the midpoint of the line joining (6, 18) and (16, 6)? (a) (11, 12) (b) (22, 24) (c) (5, 6) (d) (12, 11)
21. 21.What is the distance between the points (6, 9) and (18, 4)? (a) 169 (b) 13 (c) 14 (d) 17
22. 22.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
23. 23.What is the distance between the points (5, 15) and (10, 3)? (a) 17 (b) 14 (c) 169 (d) 13
24. 24.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
25. 25.In which quadrant does the point (−8, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
26. 26.What is the midpoint of the line joining (4, 9) and (10, 13)? (a) (11, 7) (b) (3, 2) (c) (14, 22) (d) (7, 11)
27. 27.In which quadrant does the point (7, −5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
28. 28.What is the distance between the points (5, 0) and (14, 12)? (a) 15 (b) 225 (c) 21 (d) 16
29. 29.What is the distance between the points (0, 13) and (12, 4)? (a) 225 (b) 16 (c) 21 (d) 15
30. 30.What is the distance between the points (2, 5) and (10, 11)? (a) 10 (b) 14 (c) 100 (d) 11
31. 31.What is the distance between the points (1, 2) and (7, 10)? (a) 11 (b) 100 (c) 10 (d) 14
32. 32.What is the midpoint of the line joining (3, 13) and (5, 3)? (a) (8, 4) (b) (1, 5) (c) (4, 8) (d) (8, 16)
33. 33.What is the distance between the points (4, 15) and (28, 8)? (a) 25 (b) 31 (c) 625 (d) 26
34. 34.In which quadrant does the point (−6, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
35. 35.What is the midpoint of the line joining (10, 5) and (20, 1)? (a) (30, 6) (b) (15, 3) (c) (3, 15) (d) (5, 2)
36. 36.In which quadrant does the point (4, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
37. 37.In which quadrant does the point (−1, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
38. 38.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
39. 39.In which quadrant does the point (−1, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
40. 40.In which quadrant does the point (7, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant

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