Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 697 · 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 (8, 1) and (12, 4)? (a) 6 (b) 25 (c) 5 (d) 7
2. 2.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
3. 3.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
4. 4.What is the midpoint of the line joining (1, 0) and (5, 10)? (a) (2, 5) (b) (3, 5) (c) (5, 3) (d) (6, 10)
5. 5.What is the distance between the points (0, 4) and (15, 12)? (a) 17 (b) 289 (c) 23 (d) 18
6. 6.What is the midpoint of the line joining (9, 0) and (21, 12)? (a) (6, 6) (b) (15, 6) (c) (30, 12) (d) (6, 15)
7. 7.What is the distance between the points (0, 6) and (5, 18)? (a) 14 (b) 17 (c) 13 (d) 169
8. 8.What is the midpoint of the line joining (9, 9) and (15, 15)? (a) (13, 12) (b) (12, 12) (c) (24, 24) (d) (3, 3)
9. 9.In which quadrant does the point (−2, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
10. 10.What is the distance between the points (6, 10) and (30, 3)? (a) 26 (b) 25 (c) 625 (d) 31
11. 11.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
12. 12.What is the midpoint of the line joining (2, 0) and (8, 8)? (a) (3, 4) (b) (4, 5) (c) (10, 8) (d) (5, 4)
13. 13.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
14. 14.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
15. 15.What is the midpoint of the line joining (4, 1) and (6, 5)? (a) (3, 5) (b) (5, 3) (c) (1, 2) (d) (10, 6)
16. 16.What is the distance between the points (0, 4) and (7, 28)? (a) 31 (b) 26 (c) 625 (d) 25
17. 17.What is the distance between the points (6, 14) and (22, 2)? (a) 28 (b) 400 (c) 20 (d) 21
18. 18.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
19. 19.What is the distance between the points (2, 6) and (10, 21)? (a) 18 (b) 23 (c) 17 (d) 289
20. 20.In which quadrant does the point (5, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
21. 21.What is the midpoint of the line joining (0, 16) and (10, 8)? (a) (12, 5) (b) (10, 24) (c) (5, 4) (d) (5, 12)
22. 22.What is the distance between the points (4, 6) and (16, 22)? (a) 20 (b) 400 (c) 21 (d) 28
23. 23.In which quadrant does the point (1, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
24. 24.What is the distance between the points (1, 4) and (16, 12)? (a) 17 (b) 289 (c) 23 (d) 18
25. 25.What is the distance between the points (0, 2) and (9, 14)? (a) 225 (b) 16 (c) 21 (d) 15
26. 26.What is the distance between the points (2, 12) and (14, 7)? (a) 17 (b) 169 (c) 14 (d) 13
27. 27.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
28. 28.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
29. 29.What is the distance between the points (2, 9) and (14, 14)? (a) 17 (b) 169 (c) 14 (d) 13
30. 30.In which quadrant does the point (−3, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
31. 31.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
32. 32.What is the distance between the points (4, 9) and (19, 1)? (a) 23 (b) 17 (c) 18 (d) 289
33. 33.What is the distance between the points (6, 3) and (18, 12)? (a) 15 (b) 16 (c) 225 (d) 21
34. 34.In which quadrant does the point (−2, 5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
35. 35.What is the midpoint of the line joining (7, 1) and (13, 13)? (a) (7, 10) (b) (10, 7) (c) (3, 6) (d) (20, 14)
36. 36.What is the midpoint of the line joining (4, 8) and (10, 20)? (a) (14, 28) (b) (3, 6) (c) (7, 14) (d) (14, 7)
37. 37.In which quadrant does the point (−5, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
38. 38.What is the distance between the points (6, 6) and (12, 14)? (a) 100 (b) 14 (c) 11 (d) 10
39. 39.In which quadrant does the point (7, −6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
40. 40.What is the distance between the points (0, 11) and (3, 7)? (a) 25 (b) 7 (c) 5 (d) 6

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