Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 46 · 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 distance between the points (4, 0) and (16, 5)? (a) 169 (b) 17 (c) 13 (d) 14
2. 2.What is the midpoint of the line joining (0, 9) and (6, 3)? (a) (3, 6) (b) (3, 3) (c) (6, 3) (d) (6, 12)
3. 3.What is the distance between the points (0, 3) and (12, 19)? (a) 400 (b) 21 (c) 20 (d) 28
4. 4.What is the midpoint of the line joining (5, 15) and (11, 7)? (a) (3, 4) (b) (11, 8) (c) (16, 22) (d) (8, 11)
5. 5.What is the midpoint of the line joining (7, 2) and (19, 8)? (a) (26, 10) (b) (6, 3) (c) (13, 5) (d) (5, 13)
6. 6.What is the midpoint of the line joining (5, 15) and (7, 9)? (a) (1, 3) (b) (12, 6) (c) (6, 12) (d) (12, 24)
7. 7.What is the distance between the points (2, 14) and (14, 9)? (a) 169 (b) 14 (c) 17 (d) 13
8. 8.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
9. 9.In which quadrant does the point (−7, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
10. 10.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
11. 11.In which quadrant does the point (4, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
12. 12.What is the midpoint of the line joining (4, 6) and (14, 2)? (a) (18, 8) (b) (4, 9) (c) (5, 2) (d) (9, 4)
13. 13.What is the distance between the points (1, 22) and (13, 6)? (a) 20 (b) 400 (c) 21 (d) 28
14. 14.What is the distance between the points (7, 13) and (10, 9)? (a) 7 (b) 6 (c) 25 (d) 5
15. 15.What is the distance between the points (7, 12) and (22, 4)? (a) 17 (b) 289 (c) 18 (d) 23
16. 16.What is the distance between the points (4, 5) and (16, 0)? (a) 14 (b) 169 (c) 13 (d) 17
17. 17.What is the distance between the points (1, 9) and (7, 17)? (a) 11 (b) 100 (c) 14 (d) 10
18. 18.What is the distance between the points (2, 5) and (14, 0)? (a) 17 (b) 14 (c) 169 (d) 13
19. 19.In which quadrant does the point (−6, 9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
20. 20.What is the distance between the points (4, 19) and (20, 7)? (a) 20 (b) 21 (c) 400 (d) 28
21. 21.In which quadrant does the point (−6, −6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
22. 22.What is the distance between the points (2, 6) and (14, 15)? (a) 16 (b) 225 (c) 15 (d) 21
23. 23.What is the midpoint of the line joining (6, 12) and (16, 10)? (a) (12, 11) (b) (5, 1) (c) (22, 22) (d) (11, 11)
24. 24.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
25. 25.What is the distance between the points (0, 21) and (9, 9)? (a) 21 (b) 16 (c) 225 (d) 15
26. 26.What is the midpoint of the line joining (1, 6) and (11, 2)? (a) (5, 2) (b) (4, 6) (c) (12, 8) (d) (6, 4)
27. 27.What is the midpoint of the line joining (6, 5) and (14, 1)? (a) (3, 10) (b) (4, 2) (c) (10, 3) (d) (20, 6)
28. 28.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
29. 29.What is the midpoint of the line joining (1, 8) and (13, 12)? (a) (10, 7) (b) (6, 2) (c) (14, 20) (d) (7, 10)
30. 30.What is the midpoint of the line joining (6, 6) and (16, 4)? (a) (22, 10) (b) (11, 5) (c) (5, 1) (d) (5, 11)
31. 31.What is the distance between the points (2, 12) and (14, 3)? (a) 16 (b) 225 (c) 21 (d) 15
32. 32.What is the midpoint of the line joining (1, 11) and (9, 9)? (a) (10, 5) (b) (4, 1) (c) (5, 10) (d) (10, 20)
33. 33.What is the distance between the points (8, 17) and (16, 2)? (a) 289 (b) 23 (c) 17 (d) 18
34. 34.What is the distance between the points (0, 25) and (7, 1)? (a) 31 (b) 625 (c) 26 (d) 25
35. 35.What is the midpoint of the line joining (5, 7) and (15, 15)? (a) (11, 10) (b) (10, 11) (c) (20, 22) (d) (5, 4)
36. 36.What is the midpoint of the line joining (7, 4) and (9, 2)? (a) (8, 3) (b) (3, 8) (c) (1, 1) (d) (16, 6)
37. 37.What is the distance between the points (8, 7) and (32, 14)? (a) 26 (b) 625 (c) 25 (d) 31
38. 38.What is the distance between the points (7, 4) and (10, 0)? (a) 6 (b) 7 (c) 25 (d) 5
39. 39.In which quadrant does the point (−8, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
40. 40.In which quadrant does the point (−6, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant

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