Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 198 · 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 (−2, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
2. 2.In which quadrant does the point (7, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
3. 3.What is the distance between the points (5, 12) and (10, 0)? (a) 14 (b) 13 (c) 169 (d) 17
4. 4.What is the distance between the points (1, 8) and (17, 20)? (a) 28 (b) 20 (c) 400 (d) 21
5. 5.In which quadrant does the point (1, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
6. 6.In which quadrant does the point (−2, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
7. 7.What is the midpoint of the line joining (2, 5) and (14, 11)? (a) (16, 16) (b) (8, 8) (c) (9, 8) (d) (6, 3)
8. 8.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
9. 9.What is the distance between the points (1, 17) and (13, 1)? (a) 28 (b) 21 (c) 20 (d) 400
10. 10.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
11. 11.In which quadrant does the point (8, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
12. 12.What is the distance between the points (7, 29) and (14, 5)? (a) 26 (b) 31 (c) 25 (d) 625
13. 13.What is the midpoint of the line joining (7, 4) and (11, 16)? (a) (2, 6) (b) (18, 20) (c) (10, 9) (d) (9, 10)
14. 14.In which quadrant does the point (4, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
15. 15.What is the midpoint of the line joining (1, 15) and (13, 5)? (a) (14, 20) (b) (6, 5) (c) (10, 7) (d) (7, 10)
16. 16.In which quadrant does the point (3, 1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
17. 17.What is the distance between the points (2, 5) and (11, 17)? (a) 21 (b) 15 (c) 16 (d) 225
18. 18.What is the midpoint of the line joining (4, 6) and (12, 14)? (a) (8, 10) (b) (16, 20) (c) (4, 4) (d) (10, 8)
19. 19.What is the midpoint of the line joining (9, 5) and (11, 13)? (a) (9, 10) (b) (20, 18) (c) (10, 9) (d) (1, 4)
20. 20.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
21. 21.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
22. 22.In which quadrant does the point (−2, −7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
23. 23.In which quadrant does the point (−6, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
24. 24.What is the distance between the points (1, 6) and (17, 18)? (a) 20 (b) 21 (c) 400 (d) 28
25. 25.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
26. 26.In which quadrant does the point (3, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
27. 27.What is the distance between the points (4, 2) and (12, 17)? (a) 23 (b) 17 (c) 18 (d) 289
28. 28.What is the midpoint of the line joining (5, 15) and (11, 7)? (a) (11, 8) (b) (16, 22) (c) (3, 4) (d) (8, 11)
29. 29.In which quadrant does the point (−5, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
30. 30.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
31. 31.What is the distance between the points (2, 9) and (7, 21)? (a) 169 (b) 17 (c) 13 (d) 14
32. 32.What is the distance between the points (9, 12) and (14, 0)? (a) 169 (b) 13 (c) 17 (d) 14
33. 33.What is the midpoint of the line joining (10, 15) and (12, 9)? (a) (12, 11) (b) (11, 12) (c) (1, 3) (d) (22, 24)
34. 34.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
35. 35.What is the midpoint of the line joining (2, 8) and (4, 16)? (a) (6, 24) (b) (1, 4) (c) (3, 12) (d) (12, 3)
36. 36.What is the midpoint of the line joining (3, 6) and (9, 0)? (a) (3, 6) (b) (12, 6) (c) (6, 3) (d) (3, 3)
37. 37.In which quadrant does the point (−3, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
38. 38.What is the distance between the points (4, 0) and (12, 15)? (a) 289 (b) 17 (c) 23 (d) 18
39. 39.In which quadrant does the point (4, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
40. 40.What is the distance between the points (5, 2) and (17, 18)? (a) 21 (b) 20 (c) 400 (d) 28

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