Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 987 · 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 midpoint of the line joining (4, 9) and (10, 11)? (a) (7, 10) (b) (14, 20) (c) (3, 1) (d) (10, 7)
2. 2.What is the distance between the points (1, 6) and (7, 14)? (a) 10 (b) 14 (c) 100 (d) 11
3. 3.What is the distance between the points (2, 15) and (11, 3)? (a) 21 (b) 15 (c) 16 (d) 225
4. 4.What is the distance between the points (3, 32) and (10, 8)? (a) 26 (b) 25 (c) 31 (d) 625
5. 5.What is the distance between the points (0, 21) and (9, 9)? (a) 15 (b) 21 (c) 225 (d) 16
6. 6.In which quadrant does the point (−3, −7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
7. 7.What is the midpoint of the line joining (10, 4) and (20, 14)? (a) (30, 18) (b) (15, 9) (c) (5, 5) (d) (9, 15)
8. 8.In which quadrant does the point (6, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
10. 10.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
11. 11.In which quadrant does the point (2, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
12. 12.What is the distance between the points (1, 7) and (9, 22)? (a) 289 (b) 18 (c) 17 (d) 23
13. 13.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
14. 14.What is the distance between the points (1, 7) and (6, 19)? (a) 13 (b) 169 (c) 14 (d) 17
15. 15.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
16. 16.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
17. 17.What is the midpoint of the line joining (4, 5) and (16, 17)? (a) (10, 11) (b) (20, 22) (c) (6, 6) (d) (11, 10)
18. 18.In which quadrant does the point (−3, −2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
19. 19.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
20. 20.What is the midpoint of the line joining (10, 9) and (12, 1)? (a) (11, 5) (b) (1, 4) (c) (22, 10) (d) (5, 11)
21. 21.What is the midpoint of the line joining (4, 9) and (16, 11)? (a) (11, 10) (b) (10, 10) (c) (6, 1) (d) (20, 20)
22. 22.In which quadrant does the point (5, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
23. 23.In which quadrant does the point (−9, −7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
24. 24.What is the midpoint of the line joining (9, 5) and (21, 13)? (a) (6, 4) (b) (30, 18) (c) (15, 9) (d) (9, 15)
25. 25.What is the distance between the points (3, 2) and (7, 5)? (a) 6 (b) 5 (c) 25 (d) 7
26. 26.In which quadrant does the point (−3, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
27. 27.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
28. 28.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
29. 29.In which quadrant does the point (4, −7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
30. 30.In which quadrant does the point (1, −9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
31. 31.What is the midpoint of the line joining (10, 14) and (14, 10)? (a) (24, 24) (b) (2, 2) (c) (13, 12) (d) (12, 12)
32. 32.What is the midpoint of the line joining (2, 0) and (10, 10)? (a) (12, 10) (b) (4, 5) (c) (5, 6) (d) (6, 5)
33. 33.What is the midpoint of the line joining (2, 9) and (12, 19)? (a) (14, 7) (b) (14, 28) (c) (5, 5) (d) (7, 14)
34. 34.What is the distance between the points (3, 2) and (18, 10)? (a) 18 (b) 23 (c) 17 (d) 289
35. 35.What is the midpoint of the line joining (0, 1) and (4, 5)? (a) (4, 6) (b) (3, 2) (c) (2, 3) (d) (2, 2)
36. 36.What is the midpoint of the line joining (3, 12) and (11, 2)? (a) (4, 5) (b) (8, 7) (c) (7, 7) (d) (14, 14)
37. 37.What is the distance between the points (4, 32) and (11, 8)? (a) 625 (b) 31 (c) 25 (d) 26
38. 38.What is the distance between the points (1, 6) and (16, 14)? (a) 17 (b) 18 (c) 289 (d) 23
39. 39.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
40. 40.What is the distance between the points (1, 2) and (7, 10)? (a) 11 (b) 100 (c) 10 (d) 14

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