Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 372 · 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 (1, 2) and (8, 26)? (a) 25 (b) 31 (c) 26 (d) 625
2. 2.In which quadrant does the point (−2, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
3. 3.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
4. 4.What is the distance between the points (7, 11) and (13, 3)? (a) 10 (b) 14 (c) 11 (d) 100
5. 5.What is the midpoint of the line joining (6, 4) and (18, 8)? (a) (6, 2) (b) (12, 6) (c) (6, 12) (d) (24, 12)
6. 6.In which quadrant does the point (−7, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
7. 7.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
8. 8.In which quadrant does the point (2, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
9. 9.What is the midpoint of the line joining (5, 3) and (17, 13)? (a) (8, 11) (b) (6, 5) (c) (22, 16) (d) (11, 8)
10. 10.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
11. 11.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
12. 12.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
13. 13.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
14. 14.What is the midpoint of the line joining (7, 1) and (17, 5)? (a) (3, 12) (b) (24, 6) (c) (12, 3) (d) (5, 2)
15. 15.What is the distance between the points (1, 13) and (6, 1)? (a) 13 (b) 14 (c) 17 (d) 169
16. 16.What is the midpoint of the line joining (3, 13) and (11, 9)? (a) (4, 2) (b) (14, 22) (c) (11, 7) (d) (7, 11)
17. 17.What is the midpoint of the line joining (0, 1) and (10, 5)? (a) (5, 3) (b) (5, 2) (c) (3, 5) (d) (10, 6)
18. 18.What is the distance between the points (8, 11) and (12, 8)? (a) 7 (b) 5 (c) 25 (d) 6
19. 19.What is the midpoint of the line joining (3, 12) and (5, 6)? (a) (9, 4) (b) (1, 3) (c) (8, 18) (d) (4, 9)
20. 20.What is the midpoint of the line joining (8, 14) and (20, 4)? (a) (6, 5) (b) (9, 14) (c) (28, 18) (d) (14, 9)
21. 21.In which quadrant does the point (1, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
22. 22.What is the midpoint of the line joining (3, 5) and (5, 9)? (a) (1, 2) (b) (7, 4) (c) (8, 14) (d) (4, 7)
23. 23.What is the midpoint of the line joining (9, 14) and (19, 6)? (a) (10, 14) (b) (5, 4) (c) (28, 20) (d) (14, 10)
24. 24.What is the midpoint of the line joining (9, 16) and (21, 8)? (a) (6, 4) (b) (15, 12) (c) (12, 15) (d) (30, 24)
25. 25.What is the distance between the points (1, 12) and (6, 0)? (a) 169 (b) 13 (c) 17 (d) 14
26. 26.What is the distance between the points (9, 17) and (18, 5)? (a) 21 (b) 16 (c) 15 (d) 225
27. 27.In which quadrant does the point (8, −5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
28. 28.What is the midpoint of the line joining (6, 14) and (10, 4)? (a) (8, 9) (b) (9, 8) (c) (2, 5) (d) (16, 18)
29. 29.What is the midpoint of the line joining (1, 7) and (9, 5)? (a) (5, 6) (b) (10, 12) (c) (4, 1) (d) (6, 5)
30. 30.In which quadrant does the point (6, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
31. 31.What is the midpoint of the line joining (1, 7) and (11, 11)? (a) (12, 18) (b) (6, 9) (c) (9, 6) (d) (5, 2)
32. 32.What is the midpoint of the line joining (2, 21) and (6, 9)? (a) (2, 6) (b) (15, 4) (c) (8, 30) (d) (4, 15)
33. 33.What is the distance between the points (1, 19) and (9, 4)? (a) 17 (b) 23 (c) 289 (d) 18
34. 34.What is the distance between the points (0, 17) and (12, 1)? (a) 28 (b) 400 (c) 21 (d) 20
35. 35.In which quadrant does the point (2, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
36. 36.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
37. 37.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 14 (d) 169
38. 38.What is the midpoint of the line joining (10, 6) and (14, 12)? (a) (9, 12) (b) (12, 9) (c) (24, 18) (d) (2, 3)
39. 39.In which quadrant does the point (8, 1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
40. 40.In which quadrant does the point (−1, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant

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