Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 298 · 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 (−2, −9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
2. 2.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
3. 3.In which quadrant does the point (5, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
4. 4.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
5. 5.What is the midpoint of the line joining (0, 13) and (6, 5)? (a) (9, 3) (b) (3, 4) (c) (6, 18) (d) (3, 9)
6. 6.In which quadrant does the point (9, 9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
7. 7.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
8. 8.In which quadrant does the point (3, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
9. 9.What is the distance between the points (7, 2) and (12, 14)? (a) 169 (b) 13 (c) 14 (d) 17
10. 10.In which quadrant does the point (2, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
11. 11.In which quadrant does the point (8, 5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
12. 12.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
13. 13.What is the midpoint of the line joining (2, 9) and (14, 7)? (a) (8, 8) (b) (9, 8) (c) (6, 1) (d) (16, 16)
14. 14.What is the midpoint of the line joining (7, 7) and (19, 1)? (a) (13, 4) (b) (26, 8) (c) (6, 3) (d) (4, 13)
15. 15.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
16. 16.What is the distance between the points (6, 19) and (11, 7)? (a) 17 (b) 169 (c) 14 (d) 13
17. 17.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
18. 18.In which quadrant does the point (4, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
19. 19.What is the distance between the points (6, 5) and (14, 11)? (a) 100 (b) 11 (c) 14 (d) 10
20. 20.What is the distance between the points (4, 13) and (10, 5)? (a) 100 (b) 11 (c) 10 (d) 14
21. 21.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
22. 22.What is the distance between the points (7, 7) and (19, 23)? (a) 28 (b) 400 (c) 20 (d) 21
23. 23.What is the midpoint of the line joining (7, 0) and (9, 12)? (a) (16, 12) (b) (1, 6) (c) (6, 8) (d) (8, 6)
24. 24.What is the midpoint of the line joining (9, 1) and (13, 7)? (a) (4, 11) (b) (11, 4) (c) (2, 3) (d) (22, 8)
25. 25.What is the distance between the points (6, 3) and (30, 10)? (a) 25 (b) 31 (c) 625 (d) 26
26. 26.What is the distance between the points (7, 0) and (13, 8)? (a) 14 (b) 10 (c) 100 (d) 11
27. 27.In which quadrant does the point (−3, −1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
28. 28.In which quadrant does the point (4, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
29. 29.What is the midpoint of the line joining (10, 4) and (20, 8)? (a) (5, 2) (b) (15, 6) (c) (6, 15) (d) (30, 12)
30. 30.In which quadrant does the point (7, 1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
31. 31.In which quadrant does the point (2, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
32. 32.In which quadrant does the point (9, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
33. 33.What is the distance between the points (0, 13) and (9, 1)? (a) 21 (b) 15 (c) 16 (d) 225
34. 34.In which quadrant does the point (4, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
35. 35.In which quadrant does the point (6, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
36. 36.In which quadrant does the point (6, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
37. 37.What is the midpoint of the line joining (7, 8) and (13, 10)? (a) (9, 10) (b) (3, 1) (c) (20, 18) (d) (10, 9)
38. 38.In which quadrant does the point (−1, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
39. 39.What is the distance between the points (3, 19) and (8, 7)? (a) 17 (b) 169 (c) 13 (d) 14
40. 40.In which quadrant does the point (1, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant

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