Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 749 · 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 (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
2. 2.What is the distance between the points (9, 10) and (13, 7)? (a) 7 (b) 6 (c) 25 (d) 5
3. 3.What is the distance between the points (3, 8) and (9, 0)? (a) 11 (b) 14 (c) 10 (d) 100
4. 4.What is the distance between the points (4, 10) and (8, 7)? (a) 6 (b) 7 (c) 5 (d) 25
5. 5.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
6. 6.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
7. 7.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
8. 8.What is the distance between the points (1, 15) and (7, 7)? (a) 100 (b) 14 (c) 11 (d) 10
9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
10. 10.What is the distance between the points (8, 2) and (15, 26)? (a) 25 (b) 26 (c) 625 (d) 31
11. 11.In which quadrant does the point (2, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
12. 12.In which quadrant does the point (−6, −3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
13. 13.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
14. 14.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
15. 15.What is the distance between the points (0, 3) and (4, 6)? (a) 5 (b) 25 (c) 7 (d) 6
16. 16.What is the midpoint of the line joining (8, 14) and (12, 8)? (a) (2, 3) (b) (20, 22) (c) (10, 11) (d) (11, 10)
17. 17.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
18. 18.What is the midpoint of the line joining (5, 18) and (7, 6)? (a) (1, 6) (b) (6, 12) (c) (12, 6) (d) (12, 24)
19. 19.What is the distance between the points (5, 7) and (11, 15)? (a) 11 (b) 14 (c) 10 (d) 100
20. 20.What is the midpoint of the line joining (3, 22) and (7, 10)? (a) (2, 6) (b) (5, 16) (c) (10, 32) (d) (16, 5)
21. 21.What is the distance between the points (5, 3) and (9, 0)? (a) 6 (b) 25 (c) 7 (d) 5
22. 22.What is the distance between the points (6, 1) and (18, 10)? (a) 225 (b) 21 (c) 16 (d) 15
23. 23.What is the distance between the points (1, 4) and (13, 13)? (a) 21 (b) 15 (c) 225 (d) 16
24. 24.In which quadrant does the point (8, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
25. 25.In which quadrant does the point (5, 9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
26. 26.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
27. 27.In which quadrant does the point (1, −6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
28. 28.What is the distance between the points (4, 7) and (16, 2)? (a) 169 (b) 17 (c) 14 (d) 13
29. 29.What is the distance between the points (4, 9) and (20, 21)? (a) 28 (b) 400 (c) 20 (d) 21
30. 30.What is the midpoint of the line joining (4, 9) and (8, 17)? (a) (12, 26) (b) (6, 13) (c) (2, 4) (d) (13, 6)
31. 31.What is the distance between the points (1, 5) and (4, 1)? (a) 6 (b) 5 (c) 7 (d) 25
32. 32.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
33. 33.What is the midpoint of the line joining (7, 8) and (11, 6)? (a) (18, 14) (b) (2, 1) (c) (7, 9) (d) (9, 7)
34. 34.What is the midpoint of the line joining (7, 1) and (9, 11)? (a) (6, 8) (b) (16, 12) (c) (8, 6) (d) (1, 5)
35. 35.What is the midpoint of the line joining (10, 10) and (18, 0)? (a) (5, 14) (b) (4, 5) (c) (14, 5) (d) (28, 10)
36. 36.What is the distance between the points (4, 8) and (10, 0)? (a) 14 (b) 100 (c) 10 (d) 11
37. 37.In which quadrant does the point (9, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
38. 38.In which quadrant does the point (−1, −4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
39. 39.In which quadrant does the point (2, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
40. 40.What is the midpoint of the line joining (10, 2) and (22, 14)? (a) (6, 6) (b) (16, 8) (c) (32, 16) (d) (8, 16)

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