Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 271 · 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 (−7, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
2. 2.What is the midpoint of the line joining (4, 18) and (14, 6)? (a) (12, 9) (b) (5, 6) (c) (18, 24) (d) (9, 12)
3. 3.What is the distance between the points (2, 0) and (5, 4)? (a) 25 (b) 6 (c) 7 (d) 5
4. 4.What is the distance between the points (7, 25) and (14, 1)? (a) 625 (b) 31 (c) 26 (d) 25
5. 5.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
6. 6.What is the midpoint of the line joining (10, 12) and (12, 0)? (a) (6, 11) (b) (1, 6) (c) (22, 12) (d) (11, 6)
7. 7.What is the distance between the points (9, 29) and (16, 5)? (a) 26 (b) 25 (c) 625 (d) 31
8. 8.What is the distance between the points (7, 6) and (19, 22)? (a) 28 (b) 400 (c) 21 (d) 20
9. 9.What is the distance between the points (3, 3) and (12, 15)? (a) 16 (b) 225 (c) 15 (d) 21
10. 10.What is the midpoint of the line joining (4, 2) and (10, 6)? (a) (14, 8) (b) (4, 7) (c) (3, 2) (d) (7, 4)
11. 11.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
12. 12.What is the midpoint of the line joining (2, 0) and (6, 2)? (a) (1, 4) (b) (8, 2) (c) (4, 1) (d) (2, 1)
13. 13.What is the midpoint of the line joining (4, 15) and (12, 3)? (a) (4, 6) (b) (8, 9) (c) (9, 8) (d) (16, 18)
14. 14.What is the distance between the points (6, 4) and (9, 0)? (a) 5 (b) 6 (c) 7 (d) 25
15. 15.In which quadrant does the point (7, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
16. 16.In which quadrant does the point (−7, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
17. 17.What is the midpoint of the line joining (9, 18) and (19, 6)? (a) (14, 12) (b) (5, 6) (c) (28, 24) (d) (12, 14)
18. 18.What is the distance between the points (8, 0) and (17, 12)? (a) 16 (b) 15 (c) 225 (d) 21
19. 19.What is the distance between the points (7, 31) and (14, 7)? (a) 625 (b) 31 (c) 26 (d) 25
20. 20.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
21. 21.In which quadrant does the point (−1, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
22. 22.What is the distance between the points (5, 24) and (12, 0)? (a) 25 (b) 31 (c) 26 (d) 625
23. 23.What is the distance between the points (6, 14) and (14, 8)? (a) 100 (b) 10 (c) 11 (d) 14
24. 24.What is the midpoint of the line joining (2, 13) and (4, 9)? (a) (1, 2) (b) (11, 3) (c) (6, 22) (d) (3, 11)
25. 25.What is the distance between the points (7, 2) and (19, 18)? (a) 400 (b) 20 (c) 28 (d) 21
26. 26.What is the distance between the points (3, 15) and (8, 3)? (a) 17 (b) 169 (c) 13 (d) 14
27. 27.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
28. 28.What is the midpoint of the line joining (2, 7) and (10, 17)? (a) (12, 24) (b) (4, 5) (c) (12, 6) (d) (6, 12)
29. 29.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
30. 30.What is the distance between the points (6, 30) and (13, 6)? (a) 25 (b) 625 (c) 31 (d) 26
31. 31.What is the midpoint of the line joining (8, 14) and (10, 10)? (a) (1, 2) (b) (12, 9) (c) (18, 24) (d) (9, 12)
32. 32.In which quadrant does the point (−2, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
33. 33.What is the midpoint of the line joining (4, 9) and (10, 3)? (a) (6, 7) (b) (3, 3) (c) (7, 6) (d) (14, 12)
34. 34.What is the distance between the points (5, 0) and (14, 12)? (a) 21 (b) 15 (c) 16 (d) 225
35. 35.What is the midpoint of the line joining (0, 5) and (2, 3)? (a) (1, 1) (b) (2, 8) (c) (4, 1) (d) (1, 4)
36. 36.What is the distance between the points (1, 1) and (8, 25)? (a) 31 (b) 25 (c) 26 (d) 625
37. 37.What is the distance between the points (3, 15) and (9, 7)? (a) 14 (b) 100 (c) 11 (d) 10
38. 38.What is the distance between the points (4, 9) and (19, 1)? (a) 17 (b) 289 (c) 23 (d) 18
39. 39.What is the distance between the points (5, 6) and (10, 18)? (a) 169 (b) 17 (c) 13 (d) 14
40. 40.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5

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