Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 708 · 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 distance between the points (3, 1) and (19, 13)? (a) 21 (b) 28 (c) 400 (d) 20
2. 2.What is the distance between the points (2, 16) and (11, 4)? (a) 16 (b) 225 (c) 15 (d) 21
3. 3.What is the midpoint of the line joining (0, 10) and (8, 20)? (a) (4, 15) (b) (4, 5) (c) (8, 30) (d) (15, 4)
4. 4.In which quadrant does the point (8, −5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
5. 5.What is the midpoint of the line joining (8, 8) and (12, 10)? (a) (10, 9) (b) (2, 1) (c) (20, 18) (d) (9, 10)
6. 6.What is the midpoint of the line joining (10, 2) and (18, 10)? (a) (28, 12) (b) (4, 4) (c) (14, 6) (d) (6, 14)
7. 7.What is the midpoint of the line joining (7, 0) and (9, 2)? (a) (16, 2) (b) (8, 1) (c) (1, 8) (d) (1, 1)
8. 8.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
9. 9.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
10. 10.In which quadrant does the point (8, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
11. 11.What is the distance between the points (2, 9) and (26, 2)? (a) 625 (b) 26 (c) 31 (d) 25
12. 12.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
13. 13.What is the distance between the points (0, 7) and (15, 15)? (a) 17 (b) 18 (c) 23 (d) 289
14. 14.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
15. 15.In which quadrant does the point (3, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
16. 16.What is the midpoint of the line joining (0, 16) and (2, 8)? (a) (12, 1) (b) (1, 12) (c) (2, 24) (d) (1, 4)
17. 17.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
18. 18.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
19. 19.What is the distance between the points (2, 10) and (14, 5)? (a) 13 (b) 17 (c) 169 (d) 14
20. 20.What is the distance between the points (5, 19) and (21, 7)? (a) 28 (b) 400 (c) 20 (d) 21
21. 21.What is the distance between the points (3, 9) and (8, 21)? (a) 14 (b) 169 (c) 17 (d) 13
22. 22.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
23. 23.In which quadrant does the point (−7, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
24. 24.What is the midpoint of the line joining (3, 18) and (5, 10)? (a) (8, 28) (b) (1, 4) (c) (4, 14) (d) (14, 4)
25. 25.What is the midpoint of the line joining (2, 3) and (10, 11)? (a) (4, 4) (b) (7, 6) (c) (12, 14) (d) (6, 7)
26. 26.In which quadrant does the point (7, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
27. 27.In which quadrant does the point (3, 8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
28. 28.What is the distance between the points (2, 13) and (8, 5)? (a) 10 (b) 14 (c) 11 (d) 100
29. 29.What is the distance between the points (8, 7) and (20, 16)? (a) 21 (b) 16 (c) 225 (d) 15
30. 30.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
31. 31.What is the distance between the points (8, 0) and (13, 12)? (a) 13 (b) 169 (c) 17 (d) 14
32. 32.What is the distance between the points (3, 5) and (19, 17)? (a) 28 (b) 21 (c) 20 (d) 400
33. 33.What is the distance between the points (0, 0) and (16, 12)? (a) 20 (b) 21 (c) 400 (d) 28
34. 34.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
35. 35.What is the midpoint of the line joining (5, 16) and (9, 6)? (a) (14, 22) (b) (11, 7) (c) (2, 5) (d) (7, 11)
36. 36.In which quadrant does the point (7, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
37. 37.What is the distance between the points (9, 4) and (15, 12)? (a) 11 (b) 14 (c) 100 (d) 10
38. 38.In which quadrant does the point (9, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
39. 39.What is the midpoint of the line joining (6, 0) and (8, 2)? (a) (7, 1) (b) (1, 1) (c) (14, 2) (d) (1, 7)
40. 40.In which quadrant does the point (−7, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant

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