Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 416 · 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 (0, 1) and (8, 7)? (a) (4, 4) (b) (8, 8) (c) (5, 4) (d) (4, 3)
2. 2.What is the midpoint of the line joining (0, 10) and (4, 0)? (a) (3, 5) (b) (5, 2) (c) (2, 5) (d) (4, 10)
3. 3.In which quadrant does the point (−8, −5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
4. 4.What is the midpoint of the line joining (0, 2) and (10, 0)? (a) (5, 1) (b) (10, 2) (c) (1, 5) (d) (6, 1)
5. 5.In which quadrant does the point (4, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
6. 6.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
7. 7.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 17 (d) 23
8. 8.In which quadrant does the point (3, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
9. 9.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
10. 10.What is the distance between the points (4, 26) and (11, 2)? (a) 25 (b) 31 (c) 26 (d) 625
11. 11.In which quadrant does the point (5, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
12. 12.In which quadrant does the point (−9, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
13. 13.What is the distance between the points (8, 2) and (16, 17)? (a) 18 (b) 289 (c) 23 (d) 17
14. 14.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
15. 15.What is the distance between the points (7, 29) and (14, 5)? (a) 25 (b) 625 (c) 26 (d) 31
16. 16.What is the distance between the points (0, 7) and (12, 23)? (a) 28 (b) 400 (c) 20 (d) 21
17. 17.What is the distance between the points (1, 12) and (16, 4)? (a) 17 (b) 18 (c) 23 (d) 289
18. 18.What is the midpoint of the line joining (5, 20) and (13, 10)? (a) (15, 9) (b) (4, 5) (c) (18, 30) (d) (9, 15)
19. 19.In which quadrant does the point (4, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
20. 20.What is the midpoint of the line joining (3, 21) and (13, 9)? (a) (16, 30) (b) (15, 8) (c) (8, 15) (d) (5, 6)
21. 21.What is the distance between the points (0, 13) and (15, 5)? (a) 23 (b) 289 (c) 17 (d) 18
22. 22.In which quadrant does the point (1, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
23. 23.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
24. 24.What is the distance between the points (0, 4) and (7, 28)? (a) 31 (b) 26 (c) 625 (d) 25
25. 25.What is the distance between the points (5, 9) and (11, 1)? (a) 11 (b) 14 (c) 100 (d) 10
26. 26.What is the midpoint of the line joining (2, 3) and (4, 11)? (a) (3, 7) (b) (7, 3) (c) (6, 14) (d) (1, 4)
27. 27.What is the distance between the points (7, 5) and (31, 12)? (a) 31 (b) 25 (c) 26 (d) 625
28. 28.What is the distance between the points (4, 7) and (28, 14)? (a) 26 (b) 31 (c) 625 (d) 25
29. 29.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
30. 30.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
31. 31.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
32. 32.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
33. 33.What is the midpoint of the line joining (2, 3) and (8, 13)? (a) (8, 5) (b) (5, 8) (c) (10, 16) (d) (3, 5)
34. 34.In which quadrant does the point (4, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
35. 35.What is the midpoint of the line joining (7, 3) and (9, 1)? (a) (2, 8) (b) (1, 1) (c) (16, 4) (d) (8, 2)
36. 36.What is the midpoint of the line joining (8, 3) and (16, 13)? (a) (8, 12) (b) (24, 16) (c) (12, 8) (d) (4, 5)
37. 37.What is the midpoint of the line joining (3, 5) and (15, 13)? (a) (9, 9) (b) (10, 9) (c) (6, 4) (d) (18, 18)
38. 38.In which quadrant does the point (2, −7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
39. 39.What is the midpoint of the line joining (2, 3) and (4, 5)? (a) (4, 3) (b) (3, 4) (c) (1, 1) (d) (6, 8)
40. 40.In which quadrant does the point (9, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant

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