Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 117 · 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, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
2. 2.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
3. 3.What is the midpoint of the line joining (0, 17) and (2, 9)? (a) (2, 26) (b) (1, 4) (c) (1, 13) (d) (13, 1)
4. 4.In which quadrant does the point (−4, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
5. 5.What is the midpoint of the line joining (8, 8) and (12, 10)? (a) (10, 9) (b) (20, 18) (c) (9, 10) (d) (2, 1)
6. 6.What is the distance between the points (5, 9) and (13, 3)? (a) 10 (b) 100 (c) 14 (d) 11
7. 7.In which quadrant does the point (4, 5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
8. 8.What is the midpoint of the line joining (7, 10) and (13, 20)? (a) (3, 5) (b) (20, 30) (c) (15, 10) (d) (10, 15)
9. 9.In which quadrant does the point (−7, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
10. 10.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
11. 11.In which quadrant does the point (6, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
12. 12.What is the distance between the points (2, 8) and (14, 17)? (a) 15 (b) 21 (c) 225 (d) 16
13. 13.In which quadrant does the point (4, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
14. 14.In which quadrant does the point (5, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
15. 15.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
16. 16.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
17. 17.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 14 (d) 17
18. 18.In which quadrant does the point (−9, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
19. 19.What is the distance between the points (4, 6) and (16, 22)? (a) 21 (b) 20 (c) 28 (d) 400
20. 20.In which quadrant does the point (7, 3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
21. 21.What is the midpoint of the line joining (5, 6) and (17, 2)? (a) (6, 2) (b) (22, 8) (c) (4, 11) (d) (11, 4)
22. 22.What is the distance between the points (7, 9) and (16, 21)? (a) 16 (b) 15 (c) 21 (d) 225
23. 23.In which quadrant does the point (3, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
24. 24.What is the midpoint of the line joining (8, 12) and (20, 8)? (a) (14, 10) (b) (28, 20) (c) (6, 2) (d) (10, 14)
25. 25.In which quadrant does the point (9, 9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
26. 26.In which quadrant does the point (3, −6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
27. 27.In which quadrant does the point (8, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
28. 28.What is the midpoint of the line joining (10, 6) and (14, 18)? (a) (13, 12) (b) (24, 24) (c) (2, 6) (d) (12, 12)
29. 29.What is the midpoint of the line joining (7, 6) and (11, 10)? (a) (18, 16) (b) (8, 9) (c) (2, 2) (d) (9, 8)
30. 30.What is the distance between the points (5, 17) and (20, 9)? (a) 289 (b) 17 (c) 18 (d) 23
31. 31.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
32. 32.What is the distance between the points (6, 6) and (12, 14)? (a) 11 (b) 14 (c) 100 (d) 10
33. 33.What is the distance between the points (2, 5) and (14, 10)? (a) 14 (b) 17 (c) 13 (d) 169
34. 34.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
35. 35.What is the distance between the points (6, 0) and (15, 12)? (a) 15 (b) 16 (c) 21 (d) 225
36. 36.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
37. 37.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
38. 38.In which quadrant does the point (−1, −5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
39. 39.In which quadrant does the point (4, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
40. 40.In which quadrant does the point (7, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant

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