Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 196 · 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 (2, 12) and (14, 7)? (a) 169 (b) 17 (c) 13 (d) 14
2. 2.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 21 (d) 225
3. 3.What is the midpoint of the line joining (0, 9) and (6, 5)? (a) (6, 14) (b) (7, 3) (c) (3, 7) (d) (3, 2)
4. 4.In which quadrant does the point (1, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
5. 5.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
6. 6.What is the distance between the points (5, 15) and (11, 7)? (a) 100 (b) 14 (c) 11 (d) 10
7. 7.What is the distance between the points (9, 1) and (12, 5)? (a) 7 (b) 5 (c) 25 (d) 6
8. 8.In which quadrant does the point (−4, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
9. 9.In which quadrant does the point (−1, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
10. 10.What is the midpoint of the line joining (1, 3) and (13, 5)? (a) (4, 7) (b) (6, 1) (c) (14, 8) (d) (7, 4)
11. 11.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
12. 12.What is the distance between the points (3, 14) and (19, 2)? (a) 21 (b) 28 (c) 400 (d) 20
13. 13.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
14. 14.What is the distance between the points (9, 11) and (13, 8)? (a) 7 (b) 25 (c) 5 (d) 6
15. 15.What is the distance between the points (3, 9) and (15, 14)? (a) 17 (b) 169 (c) 14 (d) 13
16. 16.What is the midpoint of the line joining (1, 11) and (13, 3)? (a) (14, 14) (b) (8, 7) (c) (7, 7) (d) (6, 4)
17. 17.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
18. 18.What is the midpoint of the line joining (10, 11) and (18, 1)? (a) (4, 5) (b) (6, 14) (c) (14, 6) (d) (28, 12)
19. 19.In which quadrant does the point (−2, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
20. 20.In which quadrant does the point (−3, 5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
21. 21.What is the distance between the points (4, 22) and (12, 7)? (a) 289 (b) 17 (c) 18 (d) 23
22. 22.What is the midpoint of the line joining (8, 1) and (20, 3)? (a) (2, 14) (b) (6, 1) (c) (28, 4) (d) (14, 2)
23. 23.What is the midpoint of the line joining (2, 14) and (8, 2)? (a) (3, 6) (b) (10, 16) (c) (8, 5) (d) (5, 8)
24. 24.What is the distance between the points (2, 0) and (11, 12)? (a) 16 (b) 225 (c) 15 (d) 21
25. 25.In which quadrant does the point (4, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
26. 26.What is the midpoint of the line joining (4, 10) and (14, 6)? (a) (5, 2) (b) (9, 8) (c) (8, 9) (d) (18, 16)
27. 27.What is the distance between the points (7, 24) and (15, 9)? (a) 289 (b) 23 (c) 18 (d) 17
28. 28.What is the midpoint of the line joining (9, 11) and (19, 1)? (a) (28, 12) (b) (14, 6) (c) (6, 14) (d) (5, 5)
29. 29.What is the distance between the points (6, 6) and (13, 30)? (a) 625 (b) 25 (c) 31 (d) 26
30. 30.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
31. 31.What is the midpoint of the line joining (2, 18) and (14, 6)? (a) (12, 8) (b) (6, 6) (c) (16, 24) (d) (8, 12)
32. 32.What is the distance between the points (8, 0) and (17, 12)? (a) 15 (b) 225 (c) 16 (d) 21
33. 33.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
34. 34.In which quadrant does the point (−2, −7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
35. 35.What is the midpoint of the line joining (9, 21) and (13, 9)? (a) (2, 6) (b) (11, 15) (c) (22, 30) (d) (15, 11)
36. 36.What is the midpoint of the line joining (2, 11) and (10, 5)? (a) (8, 6) (b) (4, 3) (c) (6, 8) (d) (12, 16)
37. 37.What is the midpoint of the line joining (4, 4) and (14, 2)? (a) (3, 9) (b) (18, 6) (c) (9, 3) (d) (5, 1)
38. 38.In which quadrant does the point (6, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
39. 39.In which quadrant does the point (−1, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
40. 40.What is the midpoint of the line joining (6, 8) and (10, 14)? (a) (16, 22) (b) (2, 3) (c) (11, 8) (d) (8, 11)

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