Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 810 · 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 (−8, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
2. 2.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
3. 3.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
4. 4.What is the distance between the points (2, 2) and (10, 17)? (a) 18 (b) 23 (c) 17 (d) 289
5. 5.In which quadrant does the point (3, −9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
6. 6.What is the distance between the points (3, 0) and (7, 3)? (a) 6 (b) 5 (c) 7 (d) 25
7. 7.What is the distance between the points (0, 7) and (3, 3)? (a) 5 (b) 7 (c) 25 (d) 6
8. 8.What is the distance between the points (8, 11) and (11, 7)? (a) 6 (b) 25 (c) 7 (d) 5
9. 9.What is the distance between the points (4, 14) and (9, 2)? (a) 14 (b) 17 (c) 169 (d) 13
10. 10.In which quadrant does the point (8, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
11. 11.What is the midpoint of the line joining (1, 6) and (13, 2)? (a) (7, 4) (b) (4, 7) (c) (14, 8) (d) (6, 2)
12. 12.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
13. 13.In which quadrant does the point (−9, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
14. 14.In which quadrant does the point (−3, −8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
15. 15.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
16. 16.What is the distance between the points (0, 15) and (8, 0)? (a) 289 (b) 17 (c) 18 (d) 23
17. 17.What is the distance between the points (7, 6) and (13, 14)? (a) 100 (b) 11 (c) 14 (d) 10
18. 18.What is the midpoint of the line joining (7, 2) and (9, 12)? (a) (16, 14) (b) (8, 7) (c) (1, 5) (d) (7, 8)
19. 19.What is the distance between the points (5, 21) and (13, 6)? (a) 23 (b) 18 (c) 289 (d) 17
20. 20.What is the distance between the points (0, 3) and (24, 10)? (a) 31 (b) 25 (c) 625 (d) 26
21. 21.What is the midpoint of the line joining (10, 10) and (22, 4)? (a) (6, 3) (b) (32, 14) (c) (16, 7) (d) (7, 16)
22. 22.In which quadrant does the point (1, −2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
23. 23.What is the distance between the points (1, 9) and (4, 5)? (a) 5 (b) 6 (c) 25 (d) 7
24. 24.What is the midpoint of the line joining (5, 1) and (11, 5)? (a) (16, 6) (b) (3, 2) (c) (3, 8) (d) (8, 3)
25. 25.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
26. 26.What is the midpoint of the line joining (2, 11) and (14, 9)? (a) (8, 10) (b) (10, 8) (c) (6, 1) (d) (16, 20)
27. 27.In which quadrant does the point (3, −8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
28. 28.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
29. 29.In which quadrant does the point (5, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
30. 30.What is the distance between the points (7, 7) and (22, 15)? (a) 18 (b) 289 (c) 17 (d) 23
31. 31.In which quadrant does the point (5, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
32. 32.What is the midpoint of the line joining (2, 17) and (4, 5)? (a) (11, 3) (b) (3, 11) (c) (1, 6) (d) (6, 22)
33. 33.What is the distance between the points (9, 13) and (24, 5)? (a) 289 (b) 23 (c) 18 (d) 17
34. 34.What is the midpoint of the line joining (9, 10) and (21, 14)? (a) (15, 12) (b) (6, 2) (c) (30, 24) (d) (12, 15)
35. 35.What is the distance between the points (9, 1) and (21, 6)? (a) 169 (b) 13 (c) 14 (d) 17
36. 36.What is the distance between the points (3, 0) and (15, 5)? (a) 13 (b) 17 (c) 14 (d) 169
37. 37.In which quadrant does the point (7, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
38. 38.What is the midpoint of the line joining (8, 9) and (20, 17)? (a) (6, 4) (b) (28, 26) (c) (13, 14) (d) (14, 13)
39. 39.What is the distance between the points (1, 4) and (17, 16)? (a) 21 (b) 20 (c) 28 (d) 400
40. 40.What is the distance between the points (0, 15) and (8, 9)? (a) 14 (b) 100 (c) 11 (d) 10

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