Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 854 · 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 (2, 6) and (5, 2)? (a) 7 (b) 25 (c) 6 (d) 5
2. 2.What is the midpoint of the line joining (9, 18) and (21, 8)? (a) (30, 26) (b) (13, 15) (c) (15, 13) (d) (6, 5)
3. 3.What is the distance between the points (2, 5) and (14, 0)? (a) 14 (b) 17 (c) 169 (d) 13
4. 4.What is the distance between the points (8, 9) and (16, 24)? (a) 17 (b) 289 (c) 23 (d) 18
5. 5.What is the midpoint of the line joining (9, 2) and (21, 12)? (a) (30, 14) (b) (6, 5) (c) (7, 15) (d) (15, 7)
6. 6.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
7. 7.What is the distance between the points (6, 2) and (18, 18)? (a) 400 (b) 21 (c) 28 (d) 20
8. 8.What is the distance between the points (6, 9) and (18, 14)? (a) 169 (b) 17 (c) 13 (d) 14
9. 9.What is the midpoint of the line joining (9, 4) and (13, 0)? (a) (22, 4) (b) (2, 11) (c) (11, 2) (d) (2, 2)
10. 10.What is the distance between the points (4, 8) and (16, 13)? (a) 17 (b) 13 (c) 14 (d) 169
11. 11.What is the midpoint of the line joining (0, 10) and (2, 2)? (a) (2, 12) (b) (1, 4) (c) (1, 6) (d) (6, 1)
12. 12.What is the midpoint of the line joining (5, 1) and (7, 11)? (a) (7, 6) (b) (1, 5) (c) (12, 12) (d) (6, 6)
13. 13.What is the midpoint of the line joining (2, 6) and (4, 2)? (a) (1, 2) (b) (4, 3) (c) (6, 8) (d) (3, 4)
14. 14.In which quadrant does the point (−8, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
15. 15.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
16. 16.What is the midpoint of the line joining (5, 2) and (13, 4)? (a) (4, 1) (b) (18, 6) (c) (3, 9) (d) (9, 3)
17. 17.What is the distance between the points (1, 8) and (9, 23)? (a) 18 (b) 17 (c) 289 (d) 23
18. 18.In which quadrant does the point (−9, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
19. 19.What is the distance between the points (1, 1) and (13, 6)? (a) 17 (b) 169 (c) 13 (d) 14
20. 20.In which quadrant does the point (−6, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
21. 21.What is the distance between the points (3, 5) and (11, 11)? (a) 100 (b) 11 (c) 14 (d) 10
22. 22.In which quadrant does the point (−9, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
23. 23.What is the distance between the points (7, 3) and (10, 7)? (a) 6 (b) 25 (c) 5 (d) 7
24. 24.In which quadrant does the point (−5, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
25. 25.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
26. 26.In which quadrant does the point (2, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
27. 27.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
28. 28.In which quadrant does the point (9, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
29. 29.What is the midpoint of the line joining (1, 14) and (9, 10)? (a) (5, 12) (b) (4, 2) (c) (10, 24) (d) (12, 5)
30. 30.What is the distance between the points (5, 4) and (10, 16)? (a) 14 (b) 17 (c) 13 (d) 169
31. 31.In which quadrant does the point (7, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
32. 32.What is the distance between the points (5, 9) and (11, 1)? (a) 14 (b) 100 (c) 10 (d) 11
33. 33.What is the distance between the points (3, 19) and (8, 7)? (a) 17 (b) 169 (c) 14 (d) 13
34. 34.In which quadrant does the point (−2, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
35. 35.What is the distance between the points (5, 4) and (8, 0)? (a) 5 (b) 25 (c) 7 (d) 6
36. 36.What is the distance between the points (2, 5) and (11, 17)? (a) 225 (b) 15 (c) 16 (d) 21
37. 37.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
38. 38.What is the distance between the points (4, 16) and (28, 9)? (a) 25 (b) 26 (c) 625 (d) 31
39. 39.What is the distance between the points (3, 4) and (15, 9)? (a) 14 (b) 13 (c) 17 (d) 169
40. 40.In which quadrant does the point (−5, 9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant

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