Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 818 · 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.In which quadrant does the point (−8, −3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
2. 2.What is the midpoint of the line joining (0, 8) and (12, 6)? (a) (6, 1) (b) (6, 7) (c) (7, 6) (d) (12, 14)
3. 3.In which quadrant does the point (−7, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
4. 4.What is the distance between the points (5, 6) and (13, 12)? (a) 11 (b) 10 (c) 14 (d) 100
5. 5.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
6. 6.What is the midpoint of the line joining (6, 15) and (10, 7)? (a) (11, 8) (b) (2, 4) (c) (16, 22) (d) (8, 11)
7. 7.What is the distance between the points (0, 8) and (9, 20)? (a) 225 (b) 16 (c) 15 (d) 21
8. 8.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
9. 9.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
10. 10.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
11. 11.In which quadrant does the point (2, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
12. 12.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
13. 13.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
14. 14.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
15. 15.What is the midpoint of the line joining (1, 20) and (7, 10)? (a) (3, 5) (b) (15, 4) (c) (4, 15) (d) (8, 30)
16. 16.What is the midpoint of the line joining (8, 20) and (14, 8)? (a) (14, 11) (b) (22, 28) (c) (11, 14) (d) (3, 6)
17. 17.What is the distance between the points (4, 18) and (16, 2)? (a) 20 (b) 21 (c) 400 (d) 28
18. 18.What is the midpoint of the line joining (10, 6) and (12, 14)? (a) (22, 20) (b) (11, 10) (c) (1, 4) (d) (10, 11)
19. 19.What is the midpoint of the line joining (4, 7) and (12, 15)? (a) (4, 4) (b) (8, 11) (c) (11, 8) (d) (16, 22)
20. 20.What is the midpoint of the line joining (3, 13) and (9, 3)? (a) (3, 5) (b) (8, 6) (c) (12, 16) (d) (6, 8)
21. 21.What is the distance between the points (1, 21) and (9, 6)? (a) 17 (b) 23 (c) 18 (d) 289
22. 22.What is the distance between the points (1, 9) and (9, 15)? (a) 100 (b) 10 (c) 14 (d) 11
23. 23.What is the distance between the points (6, 8) and (13, 32)? (a) 625 (b) 26 (c) 25 (d) 31
24. 24.What is the midpoint of the line joining (1, 10) and (5, 18)? (a) (3, 14) (b) (6, 28) (c) (14, 3) (d) (2, 4)
25. 25.What is the midpoint of the line joining (2, 6) and (10, 2)? (a) (4, 2) (b) (4, 6) (c) (12, 8) (d) (6, 4)
26. 26.What is the distance between the points (2, 10) and (8, 2)? (a) 11 (b) 100 (c) 14 (d) 10
27. 27.What is the distance between the points (9, 6) and (21, 15)? (a) 21 (b) 15 (c) 16 (d) 225
28. 28.In which quadrant does the point (5, −3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
29. 29.What is the distance between the points (8, 7) and (20, 2)? (a) 169 (b) 17 (c) 14 (d) 13
30. 30.What is the distance between the points (9, 1) and (33, 8)? (a) 31 (b) 625 (c) 26 (d) 25
31. 31.In which quadrant does the point (9, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
32. 32.What is the distance between the points (8, 12) and (32, 5)? (a) 625 (b) 31 (c) 25 (d) 26
33. 33.What is the distance between the points (8, 5) and (20, 0)? (a) 169 (b) 14 (c) 13 (d) 17
34. 34.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
35. 35.In which quadrant does the point (8, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
36. 36.What is the midpoint of the line joining (1, 10) and (5, 12)? (a) (11, 3) (b) (2, 1) (c) (3, 11) (d) (6, 22)
37. 37.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
38. 38.In which quadrant does the point (−4, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
39. 39.What is the midpoint of the line joining (2, 9) and (4, 5)? (a) (6, 14) (b) (3, 7) (c) (7, 3) (d) (1, 2)
40. 40.What is the distance between the points (4, 9) and (8, 12)? (a) 6 (b) 5 (c) 7 (d) 25

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