Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 645 · 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, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
2. 2.In which quadrant does the point (−7, −9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
3. 3.In which quadrant does the point (6, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
4. 4.What is the midpoint of the line joining (10, 1) and (14, 7)? (a) (4, 12) (b) (12, 4) (c) (2, 3) (d) (24, 8)
5. 5.What is the distance between the points (4, 0) and (11, 24)? (a) 26 (b) 625 (c) 31 (d) 25
6. 6.What is the distance between the points (6, 11) and (12, 3)? (a) 14 (b) 10 (c) 100 (d) 11
7. 7.What is the distance between the points (6, 8) and (12, 16)? (a) 10 (b) 11 (c) 14 (d) 100
8. 8.What is the distance between the points (6, 18) and (18, 2)? (a) 20 (b) 400 (c) 21 (d) 28
9. 9.What is the midpoint of the line joining (10, 0) and (20, 10)? (a) (5, 5) (b) (5, 15) (c) (30, 10) (d) (15, 5)
10. 10.What is the midpoint of the line joining (7, 8) and (19, 0)? (a) (4, 13) (b) (26, 8) (c) (6, 4) (d) (13, 4)
11. 11.In which quadrant does the point (−4, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
12. 12.What is the midpoint of the line joining (3, 12) and (13, 0)? (a) (16, 12) (b) (5, 6) (c) (6, 8) (d) (8, 6)
13. 13.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
14. 14.In which quadrant does the point (7, −6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
15. 15.In which quadrant does the point (−3, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
16. 16.What is the midpoint of the line joining (9, 5) and (13, 15)? (a) (2, 5) (b) (22, 20) (c) (11, 10) (d) (10, 11)
17. 17.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
18. 18.What is the midpoint of the line joining (0, 1) and (12, 5)? (a) (3, 6) (b) (12, 6) (c) (6, 3) (d) (6, 2)
19. 19.In which quadrant does the point (4, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
20. 20.What is the distance between the points (7, 1) and (14, 25)? (a) 26 (b) 625 (c) 25 (d) 31
21. 21.What is the distance between the points (5, 13) and (13, 7)? (a) 100 (b) 11 (c) 10 (d) 14
22. 22.What is the distance between the points (8, 11) and (20, 6)? (a) 13 (b) 17 (c) 14 (d) 169
23. 23.What is the distance between the points (2, 8) and (26, 15)? (a) 31 (b) 625 (c) 26 (d) 25
24. 24.What is the distance between the points (2, 3) and (17, 11)? (a) 18 (b) 289 (c) 17 (d) 23
25. 25.What is the distance between the points (0, 1) and (7, 25)? (a) 26 (b) 25 (c) 625 (d) 31
26. 26.What is the distance between the points (6, 21) and (18, 5)? (a) 28 (b) 400 (c) 20 (d) 21
27. 27.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
28. 28.What is the midpoint of the line joining (1, 6) and (5, 18)? (a) (6, 24) (b) (3, 12) (c) (12, 3) (d) (2, 6)
29. 29.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
30. 30.What is the distance between the points (0, 2) and (8, 17)? (a) 18 (b) 23 (c) 17 (d) 289
31. 31.What is the midpoint of the line joining (2, 10) and (10, 20)? (a) (15, 6) (b) (4, 5) (c) (6, 15) (d) (12, 30)
32. 32.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
33. 33.What is the distance between the points (5, 2) and (17, 11)? (a) 225 (b) 16 (c) 15 (d) 21
34. 34.What is the distance between the points (7, 9) and (16, 21)? (a) 225 (b) 15 (c) 16 (d) 21
35. 35.What is the midpoint of the line joining (8, 2) and (18, 10)? (a) (13, 6) (b) (6, 13) (c) (26, 12) (d) (5, 4)
36. 36.In which quadrant does the point (−9, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
37. 37.What is the midpoint of the line joining (3, 11) and (9, 5)? (a) (6, 8) (b) (3, 3) (c) (8, 6) (d) (12, 16)
38. 38.What is the distance between the points (1, 27) and (8, 3)? (a) 26 (b) 25 (c) 625 (d) 31
39. 39.What is the midpoint of the line joining (4, 10) and (12, 8)? (a) (16, 18) (b) (9, 8) (c) (4, 1) (d) (8, 9)
40. 40.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625

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