Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 555 · 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 (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
2. 2.What is the distance between the points (3, 9) and (6, 13)? (a) 5 (b) 6 (c) 7 (d) 25
3. 3.What is the distance between the points (8, 7) and (16, 1)? (a) 14 (b) 100 (c) 10 (d) 11
4. 4.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
5. 5.In which quadrant does the point (9, 8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
7. 7.What is the midpoint of the line joining (4, 10) and (6, 12)? (a) (10, 22) (b) (11, 5) (c) (5, 11) (d) (1, 1)
8. 8.What is the midpoint of the line joining (5, 11) and (7, 9)? (a) (12, 20) (b) (1, 1) (c) (10, 6) (d) (6, 10)
9. 9.In which quadrant does the point (−4, −9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
10. 10.What is the distance between the points (2, 0) and (10, 6)? (a) 14 (b) 10 (c) 11 (d) 100
11. 11.What is the distance between the points (1, 3) and (9, 9)? (a) 10 (b) 100 (c) 14 (d) 11
12. 12.What is the distance between the points (8, 0) and (14, 8)? (a) 11 (b) 10 (c) 100 (d) 14
13. 13.In which quadrant does the point (9, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
14. 14.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
15. 15.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
16. 16.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
17. 17.What is the midpoint of the line joining (3, 0) and (13, 4)? (a) (5, 2) (b) (16, 4) (c) (8, 2) (d) (2, 8)
18. 18.In which quadrant does the point (8, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
19. 19.In which quadrant does the point (4, −6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
20. 20.What is the midpoint of the line joining (3, 9) and (11, 13)? (a) (14, 22) (b) (11, 7) (c) (7, 11) (d) (4, 2)
21. 21.What is the distance between the points (2, 1) and (17, 9)? (a) 18 (b) 17 (c) 23 (d) 289
22. 22.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
23. 23.In which quadrant does the point (1, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
24. 24.In which quadrant does the point (9, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
25. 25.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
26. 26.What is the midpoint of the line joining (10, 15) and (12, 3)? (a) (1, 6) (b) (11, 9) (c) (9, 11) (d) (22, 18)
27. 27.In which quadrant does the point (−7, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
28. 28.What is the distance between the points (7, 5) and (19, 21)? (a) 21 (b) 28 (c) 400 (d) 20
29. 29.In which quadrant does the point (−1, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
30. 30.What is the distance between the points (0, 13) and (6, 5)? (a) 11 (b) 10 (c) 14 (d) 100
31. 31.In which quadrant does the point (−9, 4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
32. 32.What is the midpoint of the line joining (10, 20) and (20, 8)? (a) (5, 6) (b) (15, 14) (c) (30, 28) (d) (14, 15)
33. 33.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
34. 34.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
35. 35.What is the midpoint of the line joining (8, 13) and (12, 1)? (a) (2, 6) (b) (7, 10) (c) (20, 14) (d) (10, 7)
36. 36.In which quadrant does the point (2, −6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
37. 37.What is the distance between the points (8, 6) and (16, 12)? (a) 14 (b) 11 (c) 100 (d) 10
38. 38.In which quadrant does the point (−3, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
39. 39.What is the distance between the points (0, 6) and (24, 13)? (a) 625 (b) 31 (c) 26 (d) 25
40. 40.In which quadrant does the point (8, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant

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