Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 341 · 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 (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
2. 2.What is the midpoint of the line joining (7, 2) and (11, 10)? (a) (2, 4) (b) (18, 12) (c) (9, 6) (d) (6, 9)
3. 3.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
4. 4.What is the distance between the points (9, 1) and (24, 9)? (a) 289 (b) 18 (c) 17 (d) 23
5. 5.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
6. 6.In which quadrant does the point (−2, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
7. 7.What is the midpoint of the line joining (4, 15) and (14, 5)? (a) (18, 20) (b) (10, 9) (c) (5, 5) (d) (9, 10)
8. 8.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
10. 10.What is the distance between the points (8, 20) and (13, 8)? (a) 169 (b) 14 (c) 13 (d) 17
11. 11.What is the distance between the points (8, 6) and (11, 10)? (a) 7 (b) 5 (c) 25 (d) 6
12. 12.What is the midpoint of the line joining (1, 18) and (3, 10)? (a) (1, 4) (b) (2, 14) (c) (14, 2) (d) (4, 28)
13. 13.What is the midpoint of the line joining (6, 9) and (14, 15)? (a) (20, 24) (b) (12, 10) (c) (4, 3) (d) (10, 12)
14. 14.What is the distance between the points (0, 6) and (16, 18)? (a) 21 (b) 400 (c) 28 (d) 20
15. 15.What is the distance between the points (7, 2) and (31, 9)? (a) 31 (b) 625 (c) 26 (d) 25
16. 16.What is the distance between the points (4, 6) and (10, 14)? (a) 10 (b) 11 (c) 100 (d) 14
17. 17.What is the distance between the points (0, 25) and (12, 9)? (a) 28 (b) 20 (c) 400 (d) 21
18. 18.What is the distance between the points (3, 1) and (19, 13)? (a) 28 (b) 400 (c) 20 (d) 21
19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
20. 20.What is the distance between the points (2, 0) and (8, 8)? (a) 11 (b) 100 (c) 10 (d) 14
21. 21.What is the midpoint of the line joining (8, 8) and (10, 4)? (a) (6, 9) (b) (18, 12) (c) (9, 6) (d) (1, 2)
22. 22.What is the distance between the points (0, 27) and (7, 3)? (a) 31 (b) 26 (c) 625 (d) 25
23. 23.What is the distance between the points (2, 1) and (8, 9)? (a) 11 (b) 14 (c) 100 (d) 10
24. 24.In which quadrant does the point (−7, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
25. 25.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
26. 26.What is the midpoint of the line joining (0, 15) and (8, 3)? (a) (8, 18) (b) (4, 9) (c) (4, 6) (d) (9, 4)
27. 27.What is the distance between the points (9, 3) and (15, 11)? (a) 14 (b) 11 (c) 10 (d) 100
28. 28.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
29. 29.What is the midpoint of the line joining (10, 10) and (22, 16)? (a) (13, 16) (b) (6, 3) (c) (32, 26) (d) (16, 13)
30. 30.What is the distance between the points (2, 7) and (14, 12)? (a) 14 (b) 13 (c) 17 (d) 169
31. 31.What is the midpoint of the line joining (2, 4) and (10, 8)? (a) (4, 2) (b) (7, 6) (c) (6, 6) (d) (12, 12)
32. 32.What is the distance between the points (5, 0) and (9, 3)? (a) 25 (b) 6 (c) 5 (d) 7
33. 33.What is the distance between the points (0, 8) and (12, 24)? (a) 21 (b) 28 (c) 20 (d) 400
34. 34.What is the midpoint of the line joining (8, 11) and (10, 7)? (a) (9, 9) (b) (18, 18) (c) (1, 2) (d) (10, 9)
35. 35.What is the distance between the points (4, 0) and (16, 5)? (a) 13 (b) 169 (c) 17 (d) 14
36. 36.What is the midpoint of the line joining (7, 10) and (9, 0)? (a) (5, 8) (b) (16, 10) (c) (1, 5) (d) (8, 5)
37. 37.What is the midpoint of the line joining (2, 10) and (10, 22)? (a) (4, 6) (b) (16, 6) (c) (6, 16) (d) (12, 32)
38. 38.What is the midpoint of the line joining (8, 5) and (14, 3)? (a) (11, 4) (b) (3, 1) (c) (22, 8) (d) (4, 11)
39. 39.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
40. 40.What is the midpoint of the line joining (1, 0) and (11, 6)? (a) (12, 6) (b) (3, 6) (c) (6, 3) (d) (5, 3)

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