Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 950 · 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 (6, 6) and (18, 8)? (a) (6, 1) (b) (24, 14) (c) (7, 12) (d) (12, 7)
2. 2.In which quadrant does the point (−8, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
3. 3.What is the distance between the points (5, 4) and (9, 7)? (a) 25 (b) 7 (c) 6 (d) 5
4. 4.In which quadrant does the point (−9, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
5. 5.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
6. 6.What is the distance between the points (7, 13) and (23, 1)? (a) 28 (b) 20 (c) 21 (d) 400
7. 7.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
8. 8.What is the distance between the points (8, 2) and (15, 26)? (a) 26 (b) 25 (c) 625 (d) 31
9. 9.What is the distance between the points (7, 8) and (10, 4)? (a) 25 (b) 5 (c) 6 (d) 7
10. 10.What is the distance between the points (6, 8) and (18, 13)? (a) 13 (b) 14 (c) 17 (d) 169
11. 11.In which quadrant does the point (9, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
12. 12.What is the midpoint of the line joining (10, 7) and (14, 19)? (a) (2, 6) (b) (13, 12) (c) (12, 13) (d) (24, 26)
13. 13.What is the midpoint of the line joining (0, 13) and (8, 3)? (a) (8, 16) (b) (4, 5) (c) (4, 8) (d) (8, 4)
14. 14.In which quadrant does the point (−9, −4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
15. 15.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
16. 16.What is the distance between the points (8, 10) and (23, 2)? (a) 17 (b) 289 (c) 23 (d) 18
17. 17.In which quadrant does the point (8, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
18. 18.What is the midpoint of the line joining (4, 4) and (8, 0)? (a) (2, 6) (b) (6, 2) (c) (12, 4) (d) (2, 2)
19. 19.What is the distance between the points (7, 6) and (19, 11)? (a) 14 (b) 17 (c) 169 (d) 13
20. 20.What is the distance between the points (5, 2) and (11, 10)? (a) 100 (b) 14 (c) 11 (d) 10
21. 21.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
22. 22.In which quadrant does the point (−7, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
23. 23.What is the distance between the points (2, 21) and (10, 6)? (a) 18 (b) 17 (c) 23 (d) 289
24. 24.In which quadrant does the point (9, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
25. 25.What is the distance between the points (8, 9) and (14, 17)? (a) 11 (b) 100 (c) 14 (d) 10
26. 26.What is the distance between the points (4, 9) and (10, 1)? (a) 11 (b) 100 (c) 10 (d) 14
27. 27.In which quadrant does the point (1, −3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
28. 28.What is the midpoint of the line joining (5, 10) and (9, 4)? (a) (7, 7) (b) (8, 7) (c) (2, 3) (d) (14, 14)
29. 29.What is the distance between the points (5, 4) and (14, 16)? (a) 16 (b) 21 (c) 225 (d) 15
30. 30.What is the midpoint of the line joining (1, 20) and (9, 10)? (a) (4, 5) (b) (10, 30) (c) (15, 5) (d) (5, 15)
31. 31.What is the distance between the points (5, 23) and (17, 7)? (a) 21 (b) 20 (c) 28 (d) 400
32. 32.What is the distance between the points (7, 8) and (14, 32)? (a) 26 (b) 31 (c) 625 (d) 25
33. 33.What is the distance between the points (5, 12) and (29, 5)? (a) 26 (b) 625 (c) 31 (d) 25
34. 34.In which quadrant does the point (6, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
35. 35.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
36. 36.What is the distance between the points (1, 3) and (6, 15)? (a) 169 (b) 13 (c) 17 (d) 14
37. 37.What is the midpoint of the line joining (4, 5) and (10, 11)? (a) (3, 3) (b) (14, 16) (c) (7, 8) (d) (8, 7)
38. 38.What is the midpoint of the line joining (0, 17) and (2, 7)? (a) (12, 1) (b) (2, 24) (c) (1, 12) (d) (1, 5)
39. 39.What is the distance between the points (7, 2) and (19, 7)? (a) 13 (b) 14 (c) 169 (d) 17
40. 40.What is the distance between the points (0, 1) and (12, 6)? (a) 169 (b) 17 (c) 14 (d) 13

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