Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 505 · 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.In which quadrant does the point (−7, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
2. 2.What is the distance between the points (4, 13) and (19, 5)? (a) 18 (b) 289 (c) 17 (d) 23
3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
4. 4.In which quadrant does the point (2, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
5. 5.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
6. 6.In which quadrant does the point (8, 5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
8. 8.What is the midpoint of the line joining (8, 11) and (12, 3)? (a) (2, 4) (b) (10, 7) (c) (7, 10) (d) (20, 14)
9. 9.What is the distance between the points (6, 3) and (10, 0)? (a) 5 (b) 6 (c) 7 (d) 25
10. 10.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
11. 11.What is the distance between the points (6, 9) and (18, 4)? (a) 17 (b) 14 (c) 169 (d) 13
12. 12.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
13. 13.What is the midpoint of the line joining (3, 1) and (9, 9)? (a) (12, 10) (b) (3, 4) (c) (5, 6) (d) (6, 5)
14. 14.What is the midpoint of the line joining (1, 11) and (11, 7)? (a) (6, 9) (b) (9, 6) (c) (5, 2) (d) (12, 18)
15. 15.What is the midpoint of the line joining (4, 4) and (8, 14)? (a) (12, 18) (b) (9, 6) (c) (2, 5) (d) (6, 9)
16. 16.What is the midpoint of the line joining (4, 15) and (8, 7)? (a) (11, 6) (b) (6, 11) (c) (12, 22) (d) (2, 4)
17. 17.In which quadrant does the point (−2, −3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
18. 18.What is the distance between the points (6, 9) and (11, 21)? (a) 17 (b) 169 (c) 14 (d) 13
19. 19.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
20. 20.What is the midpoint of the line joining (5, 13) and (17, 7)? (a) (10, 11) (b) (11, 10) (c) (6, 3) (d) (22, 20)
21. 21.What is the midpoint of the line joining (5, 4) and (17, 0)? (a) (6, 2) (b) (22, 4) (c) (2, 11) (d) (11, 2)
22. 22.What is the distance between the points (2, 22) and (14, 6)? (a) 28 (b) 21 (c) 20 (d) 400
23. 23.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
24. 24.What is the distance between the points (1, 9) and (7, 17)? (a) 10 (b) 14 (c) 100 (d) 11
25. 25.What is the distance between the points (3, 5) and (9, 13)? (a) 10 (b) 11 (c) 14 (d) 100
26. 26.What is the distance between the points (3, 17) and (8, 5)? (a) 13 (b) 17 (c) 14 (d) 169
27. 27.What is the distance between the points (2, 3) and (18, 15)? (a) 28 (b) 21 (c) 400 (d) 20
28. 28.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
29. 29.In which quadrant does the point (−7, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
30. 30.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
31. 31.What is the distance between the points (7, 30) and (14, 6)? (a) 31 (b) 625 (c) 25 (d) 26
32. 32.In which quadrant does the point (9, 5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
33. 33.What is the distance between the points (4, 18) and (20, 6)? (a) 28 (b) 400 (c) 20 (d) 21
34. 34.In which quadrant does the point (6, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
35. 35.What is the distance between the points (1, 13) and (16, 5)? (a) 23 (b) 18 (c) 17 (d) 289
36. 36.What is the distance between the points (0, 1) and (8, 16)? (a) 17 (b) 289 (c) 23 (d) 18
37. 37.What is the midpoint of the line joining (1, 11) and (11, 3)? (a) (5, 4) (b) (12, 14) (c) (6, 7) (d) (7, 6)
38. 38.What is the distance between the points (6, 4) and (9, 0)? (a) 7 (b) 5 (c) 6 (d) 25
39. 39.What is the distance between the points (0, 4) and (12, 9)? (a) 14 (b) 13 (c) 169 (d) 17
40. 40.In which quadrant does the point (6, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant

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