Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 408 · 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 (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
2. 2.What is the distance between the points (2, 1) and (10, 7)? (a) 14 (b) 100 (c) 11 (d) 10
3. 3.In which quadrant does the point (7, −4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
4. 4.In which quadrant does the point (−2, 8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
5. 5.In which quadrant does the point (−7, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
6. 6.What is the distance between the points (8, 5) and (14, 13)? (a) 11 (b) 100 (c) 10 (d) 14
7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
8. 8.What is the distance between the points (6, 1) and (11, 13)? (a) 169 (b) 17 (c) 14 (d) 13
9. 9.What is the distance between the points (4, 6) and (11, 30)? (a) 25 (b) 31 (c) 26 (d) 625
10. 10.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
11. 11.What is the midpoint of the line joining (7, 4) and (19, 6)? (a) (26, 10) (b) (6, 1) (c) (5, 13) (d) (13, 5)
12. 12.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
13. 13.What is the distance between the points (9, 0) and (21, 16)? (a) 20 (b) 28 (c) 400 (d) 21
14. 14.What is the distance between the points (5, 14) and (13, 8)? (a) 14 (b) 11 (c) 10 (d) 100
15. 15.In which quadrant does the point (1, 5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
16. 16.In which quadrant does the point (9, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
17. 17.What is the midpoint of the line joining (10, 18) and (18, 10)? (a) (28, 28) (b) (15, 14) (c) (4, 4) (d) (14, 14)
18. 18.What is the midpoint of the line joining (6, 2) and (16, 8)? (a) (5, 3) (b) (22, 10) (c) (5, 11) (d) (11, 5)
19. 19.What is the distance between the points (6, 3) and (10, 0)? (a) 5 (b) 25 (c) 7 (d) 6
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 (3, 1) and (13, 7)? (a) (16, 8) (b) (5, 3) (c) (8, 4) (d) (4, 8)
22. 22.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
23. 23.What is the distance between the points (9, 7) and (33, 14)? (a) 625 (b) 31 (c) 26 (d) 25
24. 24.In which quadrant does the point (3, 9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
25. 25.In which quadrant does the point (−9, 5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
26. 26.In which quadrant does the point (6, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
27. 27.In which quadrant does the point (9, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
28. 28.What is the distance between the points (2, 11) and (5, 7)? (a) 7 (b) 25 (c) 5 (d) 6
29. 29.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
30. 30.In which quadrant does the point (7, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
31. 31.What is the distance between the points (0, 6) and (8, 21)? (a) 23 (b) 18 (c) 289 (d) 17
32. 32.In which quadrant does the point (5, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
33. 33.What is the midpoint of the line joining (7, 14) and (17, 4)? (a) (12, 9) (b) (24, 18) (c) (9, 12) (d) (5, 5)
34. 34.In which quadrant does the point (5, 7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
35. 35.What is the midpoint of the line joining (7, 4) and (11, 0)? (a) (18, 4) (b) (2, 2) (c) (9, 2) (d) (2, 9)
36. 36.What is the midpoint of the line joining (1, 0) and (9, 8)? (a) (4, 5) (b) (4, 4) (c) (5, 4) (d) (10, 8)
37. 37.What is the midpoint of the line joining (0, 10) and (4, 0)? (a) (3, 5) (b) (2, 5) (c) (4, 10) (d) (5, 2)
38. 38.What is the distance between the points (2, 6) and (26, 13)? (a) 25 (b) 26 (c) 31 (d) 625
39. 39.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
40. 40.What is the distance between the points (5, 14) and (17, 5)? (a) 21 (b) 16 (c) 225 (d) 15

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