Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 265 · 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.What is the midpoint of the line joining (3, 0) and (7, 8)? (a) (10, 8) (b) (5, 4) (c) (2, 4) (d) (4, 5)
2. 2.In which quadrant does the point (3, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
3. 3.In which quadrant does the point (1, −8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
4. 4.What is the distance between the points (5, 12) and (11, 4)? (a) 100 (b) 11 (c) 14 (d) 10
5. 5.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
6. 6.What is the midpoint of the line joining (4, 0) and (6, 8)? (a) (5, 4) (b) (4, 5) (c) (10, 8) (d) (1, 4)
7. 7.What is the distance between the points (3, 3) and (8, 15)? (a) 17 (b) 169 (c) 14 (d) 13
8. 8.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
9. 9.What is the midpoint of the line joining (0, 4) and (6, 14)? (a) (3, 5) (b) (3, 9) (c) (9, 3) (d) (6, 18)
10. 10.What is the distance between the points (4, 1) and (8, 4)? (a) 7 (b) 5 (c) 6 (d) 25
11. 11.What is the midpoint of the line joining (3, 15) and (5, 7)? (a) (11, 4) (b) (4, 11) (c) (8, 22) (d) (1, 4)
12. 12.What is the distance between the points (7, 2) and (23, 14)? (a) 20 (b) 28 (c) 400 (d) 21
13. 13.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
14. 14.In which quadrant does the point (−2, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
15. 15.What is the distance between the points (9, 14) and (21, 9)? (a) 17 (b) 169 (c) 14 (d) 13
16. 16.In which quadrant does the point (1, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
17. 17.In which quadrant does the point (3, 3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
18. 18.What is the midpoint of the line joining (2, 5) and (4, 1)? (a) (1, 2) (b) (6, 6) (c) (4, 3) (d) (3, 3)
19. 19.What is the distance between the points (4, 5) and (28, 12)? (a) 26 (b) 625 (c) 25 (d) 31
20. 20.What is the distance between the points (0, 3) and (6, 11)? (a) 11 (b) 100 (c) 10 (d) 14
21. 21.What is the distance between the points (2, 5) and (5, 9)? (a) 7 (b) 5 (c) 6 (d) 25
22. 22.In which quadrant does the point (−4, 5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
23. 23.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
24. 24.What is the midpoint of the line joining (2, 15) and (8, 3)? (a) (10, 18) (b) (5, 9) (c) (3, 6) (d) (9, 5)
25. 25.What is the distance between the points (3, 7) and (10, 31)? (a) 26 (b) 625 (c) 25 (d) 31
26. 26.What is the distance between the points (7, 2) and (11, 5)? (a) 5 (b) 6 (c) 25 (d) 7
27. 27.In which quadrant does the point (6, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
28. 28.What is the midpoint of the line joining (5, 4) and (9, 12)? (a) (2, 4) (b) (14, 16) (c) (8, 7) (d) (7, 8)
29. 29.In which quadrant does the point (−6, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
30. 30.What is the distance between the points (0, 3) and (4, 6)? (a) 5 (b) 25 (c) 6 (d) 7
31. 31.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
32. 32.What is the distance between the points (3, 17) and (15, 1)? (a) 21 (b) 20 (c) 28 (d) 400
33. 33.What is the distance between the points (5, 9) and (20, 17)? (a) 289 (b) 18 (c) 23 (d) 17
34. 34.What is the midpoint of the line joining (0, 17) and (12, 7)? (a) (6, 5) (b) (12, 6) (c) (12, 24) (d) (6, 12)
35. 35.What is the distance between the points (9, 7) and (21, 23)? (a) 400 (b) 21 (c) 28 (d) 20
36. 36.In which quadrant does the point (8, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
37. 37.What is the distance between the points (9, 3) and (17, 9)? (a) 14 (b) 10 (c) 11 (d) 100
38. 38.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
39. 39.In which quadrant does the point (−1, −7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
40. 40.In which quadrant does the point (7, −6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant

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