Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 322 · 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 (3, 1) and (7, 11)? (a) (2, 5) (b) (10, 12) (c) (6, 5) (d) (5, 6)
2. 2.In which quadrant does the point (2, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
3. 3.In which quadrant does the point (1, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
4. 4.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
5. 5.What is the distance between the points (0, 9) and (24, 2)? (a) 26 (b) 31 (c) 25 (d) 625
6. 6.In which quadrant does the point (−3, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
7. 7.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
8. 8.What is the distance between the points (3, 22) and (11, 7)? (a) 17 (b) 18 (c) 23 (d) 289
9. 9.What is the midpoint of the line joining (10, 3) and (12, 7)? (a) (5, 11) (b) (11, 5) (c) (1, 2) (d) (22, 10)
10. 10.What is the midpoint of the line joining (7, 10) and (19, 18)? (a) (13, 14) (b) (26, 28) (c) (6, 4) (d) (14, 13)
11. 11.What is the distance between the points (1, 3) and (8, 27)? (a) 25 (b) 625 (c) 31 (d) 26
12. 12.What is the midpoint of the line joining (6, 14) and (12, 10)? (a) (9, 12) (b) (18, 24) (c) (12, 9) (d) (3, 2)
13. 13.In which quadrant does the point (3, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
14. 14.What is the distance between the points (2, 0) and (10, 15)? (a) 18 (b) 23 (c) 289 (d) 17
15. 15.What is the distance between the points (6, 16) and (21, 8)? (a) 289 (b) 17 (c) 23 (d) 18
16. 16.What is the midpoint of the line joining (10, 5) and (14, 7)? (a) (6, 12) (b) (12, 6) (c) (2, 1) (d) (24, 12)
17. 17.What is the midpoint of the line joining (7, 5) and (11, 17)? (a) (2, 6) (b) (9, 11) (c) (11, 9) (d) (18, 22)
18. 18.What is the midpoint of the line joining (2, 19) and (8, 9)? (a) (5, 14) (b) (14, 5) (c) (3, 5) (d) (10, 28)
19. 19.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
20. 20.What is the distance between the points (7, 17) and (19, 8)? (a) 16 (b) 21 (c) 225 (d) 15
21. 21.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
22. 22.What is the midpoint of the line joining (8, 2) and (20, 6)? (a) (14, 4) (b) (4, 14) (c) (6, 2) (d) (28, 8)
23. 23.What is the midpoint of the line joining (4, 3) and (8, 11)? (a) (2, 4) (b) (7, 6) (c) (12, 14) (d) (6, 7)
24. 24.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
25. 25.What is the midpoint of the line joining (1, 10) and (9, 4)? (a) (4, 3) (b) (10, 14) (c) (7, 5) (d) (5, 7)
26. 26.What is the midpoint of the line joining (0, 4) and (2, 16)? (a) (10, 1) (b) (1, 6) (c) (2, 20) (d) (1, 10)
27. 27.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
28. 28.What is the distance between the points (2, 7) and (10, 13)? (a) 14 (b) 100 (c) 10 (d) 11
29. 29.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
30. 30.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
31. 31.In which quadrant does the point (−2, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
32. 32.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
33. 33.What is the midpoint of the line joining (0, 9) and (2, 5)? (a) (7, 1) (b) (2, 14) (c) (1, 2) (d) (1, 7)
34. 34.In which quadrant does the point (9, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
35. 35.What is the midpoint of the line joining (1, 12) and (3, 2)? (a) (7, 2) (b) (2, 7) (c) (4, 14) (d) (1, 5)
36. 36.What is the distance between the points (6, 14) and (18, 9)? (a) 17 (b) 13 (c) 14 (d) 169
37. 37.In which quadrant does the point (8, −7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
38. 38.In which quadrant does the point (9, −1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
39. 39.What is the distance between the points (3, 8) and (12, 20)? (a) 15 (b) 16 (c) 225 (d) 21
40. 40.What is the distance between the points (8, 7) and (16, 22)? (a) 18 (b) 289 (c) 17 (d) 23

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