Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 412 · 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 (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
2. 2.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
3. 3.What is the distance between the points (1, 6) and (9, 12)? (a) 14 (b) 11 (c) 100 (d) 10
4. 4.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
5. 5.What is the midpoint of the line joining (7, 12) and (9, 4)? (a) (9, 8) (b) (16, 16) (c) (1, 4) (d) (8, 8)
6. 6.What is the distance between the points (4, 19) and (13, 7)? (a) 21 (b) 16 (c) 225 (d) 15
7. 7.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
8. 8.What is the midpoint of the line joining (0, 4) and (12, 0)? (a) (2, 6) (b) (7, 2) (c) (6, 2) (d) (12, 4)
9. 9.In which quadrant does the point (4, 3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
10. 10.In which quadrant does the point (4, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
11. 11.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
12. 12.What is the distance between the points (8, 0) and (20, 5)? (a) 17 (b) 14 (c) 13 (d) 169
13. 13.What is the midpoint of the line joining (2, 7) and (8, 11)? (a) (5, 9) (b) (9, 5) (c) (10, 18) (d) (3, 2)
14. 14.What is the distance between the points (8, 7) and (11, 3)? (a) 25 (b) 6 (c) 5 (d) 7
15. 15.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
16. 16.In which quadrant does the point (5, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
17. 17.In which quadrant does the point (−5, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
18. 18.What is the distance between the points (2, 7) and (10, 1)? (a) 14 (b) 11 (c) 100 (d) 10
19. 19.What is the distance between the points (0, 9) and (3, 5)? (a) 25 (b) 5 (c) 7 (d) 6
20. 20.What is the midpoint of the line joining (3, 0) and (13, 10)? (a) (16, 10) (b) (8, 5) (c) (5, 5) (d) (5, 8)
21. 21.What is the midpoint of the line joining (1, 8) and (11, 6)? (a) (7, 6) (b) (5, 1) (c) (6, 7) (d) (12, 14)
22. 22.What is the distance between the points (5, 3) and (12, 27)? (a) 26 (b) 625 (c) 25 (d) 31
23. 23.In which quadrant does the point (2, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
24. 24.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
25. 25.In which quadrant does the point (−7, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
26. 26.What is the distance between the points (5, 6) and (9, 9)? (a) 25 (b) 7 (c) 6 (d) 5
27. 27.What is the distance between the points (8, 9) and (16, 24)? (a) 23 (b) 17 (c) 289 (d) 18
28. 28.What is the distance between the points (0, 8) and (24, 15)? (a) 625 (b) 25 (c) 31 (d) 26
29. 29.What is the midpoint of the line joining (3, 2) and (13, 6)? (a) (4, 8) (b) (16, 8) (c) (8, 4) (d) (5, 2)
30. 30.What is the distance between the points (8, 9) and (13, 21)? (a) 13 (b) 169 (c) 17 (d) 14
31. 31.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
32. 32.What is the midpoint of the line joining (7, 2) and (15, 14)? (a) (22, 16) (b) (4, 6) (c) (11, 8) (d) (8, 11)
33. 33.What is the midpoint of the line joining (2, 4) and (4, 10)? (a) (7, 3) (b) (6, 14) (c) (1, 3) (d) (3, 7)
34. 34.What is the midpoint of the line joining (5, 16) and (11, 10)? (a) (16, 26) (b) (3, 3) (c) (8, 13) (d) (13, 8)
35. 35.What is the midpoint of the line joining (1, 2) and (11, 10)? (a) (7, 6) (b) (12, 12) (c) (5, 4) (d) (6, 6)
36. 36.In which quadrant does the point (−8, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
37. 37.What is the distance between the points (2, 12) and (11, 0)? (a) 16 (b) 21 (c) 15 (d) 225
38. 38.What is the distance between the points (0, 9) and (6, 17)? (a) 10 (b) 11 (c) 14 (d) 100
39. 39.What is the midpoint of the line joining (6, 13) and (10, 5)? (a) (16, 18) (b) (8, 9) (c) (9, 8) (d) (2, 4)
40. 40.What is the distance between the points (6, 6) and (21, 14)? (a) 18 (b) 289 (c) 23 (d) 17

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