Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 885 · 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 (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
2. 2.In which quadrant does the point (7, 9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
3. 3.What is the distance between the points (2, 13) and (7, 1)? (a) 17 (b) 169 (c) 13 (d) 14
4. 4.What is the distance between the points (7, 8) and (13, 16)? (a) 14 (b) 11 (c) 10 (d) 100
5. 5.What is the midpoint of the line joining (7, 15) and (19, 3)? (a) (13, 9) (b) (26, 18) (c) (9, 13) (d) (6, 6)
6. 6.What is the midpoint of the line joining (8, 3) and (18, 7)? (a) (26, 10) (b) (5, 2) (c) (13, 5) (d) (5, 13)
7. 7.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
8. 8.What is the midpoint of the line joining (8, 4) and (12, 16)? (a) (20, 20) (b) (10, 10) (c) (11, 10) (d) (2, 6)
9. 9.What is the midpoint of the line joining (10, 16) and (22, 10)? (a) (16, 13) (b) (13, 16) (c) (6, 3) (d) (32, 26)
10. 10.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
11. 11.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
12. 12.In which quadrant does the point (4, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
13. 13.What is the distance between the points (5, 8) and (17, 24)? (a) 20 (b) 21 (c) 400 (d) 28
14. 14.What is the distance between the points (0, 0) and (12, 9)? (a) 21 (b) 15 (c) 225 (d) 16
15. 15.What is the distance between the points (7, 13) and (15, 7)? (a) 10 (b) 100 (c) 14 (d) 11
16. 16.In which quadrant does the point (1, −2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
17. 17.In which quadrant does the point (−6, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
18. 18.In which quadrant does the point (8, 5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
19. 19.In which quadrant does the point (−1, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
20. 20.What is the midpoint of the line joining (1, 6) and (3, 8)? (a) (4, 14) (b) (2, 7) (c) (1, 1) (d) (7, 2)
21. 21.What is the distance between the points (9, 3) and (33, 10)? (a) 31 (b) 25 (c) 26 (d) 625
22. 22.In which quadrant does the point (4, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
23. 23.What is the distance between the points (9, 9) and (33, 16)? (a) 625 (b) 31 (c) 25 (d) 26
24. 24.What is the distance between the points (8, 23) and (16, 8)? (a) 18 (b) 23 (c) 17 (d) 289
25. 25.What is the distance between the points (0, 15) and (16, 3)? (a) 400 (b) 21 (c) 20 (d) 28
26. 26.What is the midpoint of the line joining (3, 1) and (11, 9)? (a) (7, 5) (b) (5, 7) (c) (14, 10) (d) (4, 4)
27. 27.In which quadrant does the point (−7, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
28. 28.What is the distance between the points (8, 13) and (20, 8)? (a) 17 (b) 14 (c) 13 (d) 169
29. 29.What is the distance between the points (0, 4) and (5, 16)? (a) 14 (b) 17 (c) 169 (d) 13
30. 30.What is the distance between the points (4, 21) and (9, 9)? (a) 14 (b) 13 (c) 169 (d) 17
31. 31.What is the midpoint of the line joining (6, 10) and (10, 18)? (a) (16, 28) (b) (2, 4) (c) (8, 14) (d) (14, 8)
32. 32.What is the distance between the points (9, 1) and (16, 25)? (a) 31 (b) 25 (c) 26 (d) 625
33. 33.In which quadrant does the point (1, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
34. 34.What is the distance between the points (9, 7) and (14, 19)? (a) 17 (b) 13 (c) 14 (d) 169
35. 35.What is the midpoint of the line joining (5, 7) and (17, 13)? (a) (22, 20) (b) (10, 11) (c) (6, 3) (d) (11, 10)
36. 36.What is the midpoint of the line joining (2, 10) and (10, 6)? (a) (8, 6) (b) (6, 8) (c) (4, 2) (d) (12, 16)
37. 37.What is the midpoint of the line joining (5, 4) and (17, 8)? (a) (22, 12) (b) (6, 11) (c) (11, 6) (d) (6, 2)
38. 38.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
39. 39.What is the distance between the points (0, 13) and (12, 8)? (a) 17 (b) 13 (c) 14 (d) 169
40. 40.What is the midpoint of the line joining (0, 11) and (10, 5)? (a) (5, 8) (b) (8, 5) (c) (5, 3) (d) (10, 16)

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