Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 136 · 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 (4, 4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
2. 2.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
3. 3.What is the distance between the points (1, 5) and (9, 20)? (a) 289 (b) 17 (c) 18 (d) 23
4. 4.What is the distance between the points (9, 5) and (21, 10)? (a) 13 (b) 17 (c) 14 (d) 169
5. 5.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
6. 6.What is the midpoint of the line joining (2, 1) and (12, 5)? (a) (3, 7) (b) (14, 6) (c) (5, 2) (d) (7, 3)
7. 7.What is the midpoint of the line joining (6, 0) and (18, 12)? (a) (6, 12) (b) (24, 12) (c) (12, 6) (d) (6, 6)
8. 8.What is the distance between the points (8, 6) and (11, 2)? (a) 6 (b) 5 (c) 7 (d) 25
9. 9.What is the midpoint of the line joining (2, 9) and (10, 5)? (a) (12, 14) (b) (6, 7) (c) (7, 6) (d) (4, 2)
10. 10.In which quadrant does the point (−8, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
11. 11.What is the midpoint of the line joining (5, 9) and (11, 13)? (a) (3, 2) (b) (11, 8) (c) (16, 22) (d) (8, 11)
12. 12.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
13. 13.What is the midpoint of the line joining (10, 1) and (18, 7)? (a) (14, 4) (b) (4, 3) (c) (4, 14) (d) (28, 8)
14. 14.In which quadrant does the point (−3, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
15. 15.What is the distance between the points (6, 12) and (9, 8)? (a) 7 (b) 25 (c) 6 (d) 5
16. 16.In which quadrant does the point (−4, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
17. 17.In which quadrant does the point (3, 6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
18. 18.What is the distance between the points (0, 8) and (7, 32)? (a) 31 (b) 625 (c) 25 (d) 26
19. 19.What is the midpoint of the line joining (7, 4) and (9, 6)? (a) (5, 8) (b) (1, 1) (c) (16, 10) (d) (8, 5)
20. 20.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
21. 21.What is the distance between the points (9, 8) and (21, 24)? (a) 21 (b) 400 (c) 20 (d) 28
22. 22.What is the midpoint of the line joining (3, 9) and (9, 1)? (a) (12, 10) (b) (3, 4) (c) (5, 6) (d) (6, 5)
23. 23.In which quadrant does the point (1, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
24. 24.In which quadrant does the point (3, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
25. 25.What is the midpoint of the line joining (3, 5) and (15, 11)? (a) (8, 9) (b) (9, 8) (c) (18, 16) (d) (6, 3)
26. 26.In which quadrant does the point (2, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
27. 27.What is the midpoint of the line joining (3, 14) and (5, 10)? (a) (1, 2) (b) (12, 4) (c) (4, 12) (d) (8, 24)
28. 28.What is the distance between the points (7, 17) and (13, 9)? (a) 100 (b) 11 (c) 10 (d) 14
29. 29.In which quadrant does the point (2, −9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
30. 30.What is the distance between the points (3, 5) and (27, 12)? (a) 25 (b) 625 (c) 31 (d) 26
31. 31.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
32. 32.In which quadrant does the point (3, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
33. 33.In which quadrant does the point (5, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
34. 34.What is the midpoint of the line joining (3, 12) and (7, 10)? (a) (2, 1) (b) (11, 5) (c) (5, 11) (d) (10, 22)
35. 35.In which quadrant does the point (−2, −9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
36. 36.What is the distance between the points (1, 9) and (7, 1)? (a) 10 (b) 11 (c) 100 (d) 14
37. 37.What is the distance between the points (1, 6) and (9, 12)? (a) 14 (b) 100 (c) 10 (d) 11
38. 38.What is the distance between the points (9, 8) and (12, 12)? (a) 7 (b) 6 (c) 5 (d) 25
39. 39.In which quadrant does the point (9, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
40. 40.What is the distance between the points (7, 7) and (15, 13)? (a) 10 (b) 11 (c) 14 (d) 100

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