Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 709 · 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 (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
3. 3.What is the midpoint of the line joining (8, 2) and (14, 12)? (a) (3, 5) (b) (7, 11) (c) (22, 14) (d) (11, 7)
4. 4.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
5. 5.What is the midpoint of the line joining (1, 10) and (5, 4)? (a) (3, 7) (b) (6, 14) (c) (2, 3) (d) (7, 3)
6. 6.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 14 (d) 169
7. 7.What is the distance between the points (2, 4) and (7, 16)? (a) 17 (b) 14 (c) 13 (d) 169
8. 8.What is the distance between the points (1, 0) and (7, 8)? (a) 14 (b) 10 (c) 11 (d) 100
9. 9.What is the distance between the points (1, 9) and (13, 0)? (a) 225 (b) 21 (c) 16 (d) 15
10. 10.What is the midpoint of the line joining (6, 5) and (8, 17)? (a) (14, 22) (b) (11, 7) (c) (7, 11) (d) (1, 6)
11. 11.What is the distance between the points (9, 11) and (13, 8)? (a) 5 (b) 7 (c) 25 (d) 6
12. 12.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
13. 13.In which quadrant does the point (−4, −2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
14. 14.What is the midpoint of the line joining (5, 5) and (7, 13)? (a) (6, 9) (b) (12, 18) (c) (9, 6) (d) (1, 4)
15. 15.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
16. 16.What is the distance between the points (4, 6) and (12, 0)? (a) 14 (b) 11 (c) 10 (d) 100
17. 17.What is the midpoint of the line joining (1, 2) and (3, 4)? (a) (4, 6) (b) (2, 3) (c) (1, 1) (d) (3, 2)
18. 18.In which quadrant does the point (−9, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
19. 19.In which quadrant does the point (4, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
20. 20.In which quadrant does the point (3, 3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
21. 21.What is the distance between the points (8, 1) and (11, 5)? (a) 25 (b) 5 (c) 6 (d) 7
22. 22.What is the distance between the points (8, 1) and (14, 9)? (a) 14 (b) 100 (c) 11 (d) 10
23. 23.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
24. 24.What is the distance between the points (2, 21) and (14, 5)? (a) 28 (b) 20 (c) 21 (d) 400
25. 25.What is the distance between the points (2, 6) and (14, 1)? (a) 14 (b) 17 (c) 169 (d) 13
26. 26.In which quadrant does the point (3, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
27. 27.What is the midpoint of the line joining (2, 3) and (14, 5)? (a) (8, 4) (b) (6, 1) (c) (4, 8) (d) (16, 8)
28. 28.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
29. 29.What is the distance between the points (5, 8) and (20, 16)? (a) 289 (b) 23 (c) 18 (d) 17
30. 30.In which quadrant does the point (6, 4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
31. 31.What is the distance between the points (3, 5) and (7, 2)? (a) 25 (b) 6 (c) 7 (d) 5
32. 32.What is the distance between the points (8, 4) and (11, 8)? (a) 5 (b) 7 (c) 6 (d) 25
33. 33.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
34. 34.What is the distance between the points (9, 9) and (21, 25)? (a) 28 (b) 21 (c) 400 (d) 20
35. 35.In which quadrant does the point (9, −1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
36. 36.What is the midpoint of the line joining (6, 4) and (8, 2)? (a) (1, 1) (b) (3, 7) (c) (14, 6) (d) (7, 3)
37. 37.What is the distance between the points (4, 9) and (16, 18)? (a) 225 (b) 21 (c) 16 (d) 15
38. 38.What is the distance between the points (2, 3) and (11, 15)? (a) 15 (b) 16 (c) 21 (d) 225
39. 39.What is the midpoint of the line joining (6, 4) and (16, 10)? (a) (7, 11) (b) (5, 3) (c) (11, 7) (d) (22, 14)
40. 40.In which quadrant does the point (−3, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant

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