Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 742 · 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.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
2. 2.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
3. 3.What is the midpoint of the line joining (9, 0) and (21, 4)? (a) (2, 15) (b) (6, 2) (c) (15, 2) (d) (30, 4)
4. 4.In which quadrant does the point (−3, −7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
5. 5.In which quadrant does the point (4, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
6. 6.What is the midpoint of the line joining (7, 3) and (13, 9)? (a) (6, 10) (b) (20, 12) (c) (10, 6) (d) (3, 3)
7. 7.What is the distance between the points (9, 8) and (12, 4)? (a) 7 (b) 6 (c) 5 (d) 25
8. 8.What is the midpoint of the line joining (0, 3) and (12, 5)? (a) (12, 8) (b) (6, 4) (c) (4, 6) (d) (6, 1)
9. 9.What is the midpoint of the line joining (1, 10) and (7, 6)? (a) (8, 4) (b) (3, 2) (c) (8, 16) (d) (4, 8)
10. 10.In which quadrant does the point (−4, −6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
11. 11.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
12. 12.What is the midpoint of the line joining (4, 13) and (12, 3)? (a) (4, 5) (b) (9, 8) (c) (8, 8) (d) (16, 16)
13. 13.What is the midpoint of the line joining (4, 6) and (10, 0)? (a) (3, 7) (b) (7, 3) (c) (14, 6) (d) (3, 3)
14. 14.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
15. 15.In which quadrant does the point (9, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
16. 16.What is the distance between the points (1, 9) and (8, 33)? (a) 625 (b) 26 (c) 31 (d) 25
17. 17.What is the distance between the points (2, 4) and (17, 12)? (a) 18 (b) 17 (c) 289 (d) 23
18. 18.In which quadrant does the point (−2, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
19. 19.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
20. 20.What is the distance between the points (6, 1) and (30, 8)? (a) 31 (b) 625 (c) 26 (d) 25
21. 21.What is the midpoint of the line joining (8, 0) and (20, 6)? (a) (14, 3) (b) (6, 3) (c) (28, 6) (d) (3, 14)
22. 22.What is the midpoint of the line joining (0, 7) and (2, 3)? (a) (2, 10) (b) (5, 1) (c) (1, 5) (d) (1, 2)
23. 23.In which quadrant does the point (7, −4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
24. 24.What is the midpoint of the line joining (3, 8) and (5, 0)? (a) (5, 4) (b) (4, 4) (c) (1, 4) (d) (8, 8)
25. 25.What is the distance between the points (0, 2) and (12, 7)? (a) 13 (b) 169 (c) 14 (d) 17
26. 26.What is the midpoint of the line joining (2, 1) and (8, 3)? (a) (3, 1) (b) (10, 4) (c) (2, 5) (d) (5, 2)
27. 27.What is the distance between the points (1, 13) and (17, 1)? (a) 20 (b) 400 (c) 21 (d) 28
28. 28.What is the midpoint of the line joining (10, 4) and (14, 8)? (a) (2, 2) (b) (12, 6) (c) (24, 12) (d) (6, 12)
29. 29.What is the distance between the points (4, 4) and (10, 12)? (a) 100 (b) 11 (c) 10 (d) 14
30. 30.What is the distance between the points (7, 0) and (13, 8)? (a) 14 (b) 10 (c) 100 (d) 11
31. 31.In which quadrant does the point (5, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
32. 32.What is the midpoint of the line joining (3, 15) and (9, 3)? (a) (9, 6) (b) (3, 6) (c) (6, 9) (d) (12, 18)
33. 33.In which quadrant does the point (−9, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
34. 34.In which quadrant does the point (9, 1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
35. 35.What is the midpoint of the line joining (4, 13) and (14, 1)? (a) (18, 14) (b) (7, 9) (c) (9, 7) (d) (5, 6)
36. 36.In which quadrant does the point (−7, −7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
37. 37.What is the distance between the points (1, 12) and (13, 7)? (a) 13 (b) 14 (c) 169 (d) 17
38. 38.In which quadrant does the point (2, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
39. 39.What is the midpoint of the line joining (10, 8) and (14, 18)? (a) (24, 26) (b) (2, 5) (c) (12, 13) (d) (13, 12)
40. 40.In which quadrant does the point (4, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant

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