Coordinate Geometry Worksheet for Maths Olympiad

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

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