Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 541 · 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 (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
2. 2.In which quadrant does the point (−1, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
3. 3.What is the midpoint of the line joining (3, 3) and (13, 7)? (a) (16, 10) (b) (8, 5) (c) (5, 8) (d) (5, 2)
4. 4.What is the midpoint of the line joining (5, 19) and (9, 7)? (a) (13, 7) (b) (14, 26) (c) (2, 6) (d) (7, 13)
5. 5.What is the midpoint of the line joining (9, 13) and (11, 5)? (a) (20, 18) (b) (10, 9) (c) (1, 4) (d) (9, 10)
6. 6.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
7. 7.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
8. 8.What is the distance between the points (5, 9) and (12, 33)? (a) 26 (b) 31 (c) 25 (d) 625
9. 9.In which quadrant does the point (−6, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
10. 10.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
11. 11.What is the distance between the points (1, 6) and (4, 10)? (a) 25 (b) 6 (c) 5 (d) 7
12. 12.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
13. 13.In which quadrant does the point (−2, −7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
14. 14.What is the distance between the points (8, 7) and (20, 23)? (a) 400 (b) 20 (c) 21 (d) 28
15. 15.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
16. 16.What is the midpoint of the line joining (3, 0) and (15, 12)? (a) (6, 9) (b) (6, 6) (c) (9, 6) (d) (18, 12)
17. 17.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
18. 18.What is the midpoint of the line joining (1, 11) and (13, 7)? (a) (6, 2) (b) (7, 9) (c) (14, 18) (d) (9, 7)
19. 19.What is the midpoint of the line joining (2, 11) and (6, 3)? (a) (4, 7) (b) (2, 4) (c) (8, 14) (d) (7, 4)
20. 20.What is the midpoint of the line joining (8, 20) and (14, 8)? (a) (3, 6) (b) (22, 28) (c) (14, 11) (d) (11, 14)
21. 21.What is the midpoint of the line joining (2, 16) and (8, 8)? (a) (12, 5) (b) (10, 24) (c) (5, 12) (d) (3, 4)
22. 22.What is the midpoint of the line joining (6, 0) and (18, 6)? (a) (12, 3) (b) (6, 3) (c) (24, 6) (d) (3, 12)
23. 23.What is the distance between the points (5, 11) and (20, 3)? (a) 18 (b) 289 (c) 17 (d) 23
24. 24.What is the distance between the points (1, 13) and (7, 5)? (a) 10 (b) 14 (c) 100 (d) 11
25. 25.In which quadrant does the point (4, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
26. 26.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
27. 27.What is the distance between the points (3, 0) and (6, 4)? (a) 25 (b) 6 (c) 5 (d) 7
28. 28.In which quadrant does the point (8, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
29. 29.In which quadrant does the point (−5, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
30. 30.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
31. 31.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
32. 32.What is the midpoint of the line joining (3, 1) and (11, 5)? (a) (3, 7) (b) (4, 2) (c) (14, 6) (d) (7, 3)
33. 33.What is the distance between the points (4, 0) and (28, 7)? (a) 25 (b) 26 (c) 31 (d) 625
34. 34.What is the midpoint of the line joining (3, 5) and (13, 3)? (a) (16, 8) (b) (5, 1) (c) (4, 8) (d) (8, 4)
35. 35.What is the distance between the points (1, 6) and (9, 0)? (a) 14 (b) 100 (c) 11 (d) 10
36. 36.What is the midpoint of the line joining (2, 20) and (12, 8)? (a) (5, 6) (b) (14, 7) (c) (7, 14) (d) (14, 28)
37. 37.What is the distance between the points (5, 5) and (13, 20)? (a) 18 (b) 23 (c) 289 (d) 17
38. 38.What is the distance between the points (5, 9) and (8, 13)? (a) 25 (b) 7 (c) 5 (d) 6
39. 39.What is the midpoint of the line joining (7, 7) and (9, 3)? (a) (16, 10) (b) (5, 8) (c) (8, 5) (d) (1, 2)
40. 40.What is the distance between the points (3, 1) and (15, 10)? (a) 21 (b) 16 (c) 15 (d) 225

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