Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 655 · 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 (7, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
2. 2.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
3. 3.What is the distance between the points (3, 14) and (8, 2)? (a) 13 (b) 169 (c) 17 (d) 14
4. 4.What is the midpoint of the line joining (0, 3) and (2, 1)? (a) (2, 4) (b) (2, 1) (c) (1, 1) (d) (1, 2)
5. 5.What is the midpoint of the line joining (5, 14) and (15, 2)? (a) (20, 16) (b) (10, 8) (c) (5, 6) (d) (8, 10)
6. 6.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
7. 7.In which quadrant does the point (−5, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
8. 8.In which quadrant does the point (−1, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
9. 9.What is the distance between the points (7, 6) and (10, 2)? (a) 25 (b) 5 (c) 7 (d) 6
10. 10.In which quadrant does the point (3, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
11. 11.What is the midpoint of the line joining (5, 8) and (11, 12)? (a) (10, 8) (b) (3, 2) (c) (8, 10) (d) (16, 20)
12. 12.What is the distance between the points (8, 0) and (20, 5)? (a) 169 (b) 14 (c) 17 (d) 13
13. 13.What is the distance between the points (2, 11) and (17, 3)? (a) 23 (b) 18 (c) 289 (d) 17
14. 14.In which quadrant does the point (1, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
15. 15.In which quadrant does the point (4, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
16. 16.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
17. 17.In which quadrant does the point (−5, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
18. 18.What is the midpoint of the line joining (4, 2) and (8, 8)? (a) (2, 3) (b) (12, 10) (c) (6, 5) (d) (5, 6)
19. 19.In which quadrant does the point (−9, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
20. 20.In which quadrant does the point (1, −8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
21. 21.What is the midpoint of the line joining (0, 11) and (2, 5)? (a) (1, 3) (b) (2, 16) (c) (8, 1) (d) (1, 8)
22. 22.What is the distance between the points (9, 21) and (14, 9)? (a) 17 (b) 13 (c) 169 (d) 14
23. 23.What is the distance between the points (4, 16) and (10, 8)? (a) 100 (b) 11 (c) 14 (d) 10
24. 24.What is the distance between the points (3, 7) and (9, 15)? (a) 11 (b) 10 (c) 100 (d) 14
25. 25.What is the distance between the points (3, 9) and (15, 14)? (a) 14 (b) 169 (c) 13 (d) 17
26. 26.What is the distance between the points (6, 7) and (14, 13)? (a) 14 (b) 100 (c) 10 (d) 11
27. 27.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
28. 28.What is the distance between the points (5, 7) and (14, 19)? (a) 16 (b) 225 (c) 15 (d) 21
29. 29.What is the distance between the points (2, 7) and (7, 19)? (a) 169 (b) 14 (c) 13 (d) 17
30. 30.What is the distance between the points (1, 8) and (5, 11)? (a) 6 (b) 5 (c) 25 (d) 7
31. 31.In which quadrant does the point (−3, 6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
32. 32.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
33. 33.What is the midpoint of the line joining (9, 5) and (19, 13)? (a) (5, 4) (b) (28, 18) (c) (9, 14) (d) (14, 9)
34. 34.What is the midpoint of the line joining (5, 2) and (11, 12)? (a) (16, 14) (b) (8, 7) (c) (3, 5) (d) (7, 8)
35. 35.In which quadrant does the point (−1, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
36. 36.What is the midpoint of the line joining (7, 6) and (15, 4)? (a) (11, 5) (b) (4, 1) (c) (22, 10) (d) (5, 11)
37. 37.What is the midpoint of the line joining (6, 6) and (10, 8)? (a) (7, 8) (b) (2, 1) (c) (8, 7) (d) (16, 14)
38. 38.What is the distance between the points (9, 8) and (21, 17)? (a) 15 (b) 225 (c) 16 (d) 21
39. 39.What is the midpoint of the line joining (10, 5) and (12, 17)? (a) (12, 11) (b) (22, 22) (c) (11, 11) (d) (1, 6)
40. 40.What is the distance between the points (2, 8) and (18, 20)? (a) 400 (b) 21 (c) 20 (d) 28

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