Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 611 · 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 (12, 15)? (a) 18 (b) 289 (c) 23 (d) 17
2. 2.What is the midpoint of the line joining (8, 6) and (14, 18)? (a) (11, 12) (b) (12, 11) (c) (3, 6) (d) (22, 24)
3. 3.In which quadrant does the point (4, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
4. 4.In which quadrant does the point (−3, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
5. 5.In which quadrant does the point (4, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
6. 6.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
7. 7.What is the midpoint of the line joining (9, 10) and (11, 12)? (a) (1, 1) (b) (10, 11) (c) (11, 10) (d) (20, 22)
8. 8.What is the midpoint of the line joining (9, 6) and (13, 2)? (a) (2, 2) (b) (11, 4) (c) (4, 11) (d) (22, 8)
9. 9.What is the distance between the points (8, 13) and (16, 7)? (a) 14 (b) 10 (c) 100 (d) 11
10. 10.What is the distance between the points (6, 1) and (18, 17)? (a) 28 (b) 21 (c) 20 (d) 400
11. 11.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
12. 12.In which quadrant does the point (−2, 8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
13. 13.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
14. 14.What is the midpoint of the line joining (9, 0) and (21, 2)? (a) (1, 15) (b) (6, 1) (c) (30, 2) (d) (15, 1)
15. 15.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
16. 16.What is the distance between the points (3, 18) and (15, 9)? (a) 16 (b) 15 (c) 225 (d) 21
17. 17.What is the distance between the points (7, 3) and (14, 27)? (a) 625 (b) 31 (c) 26 (d) 25
18. 18.What is the midpoint of the line joining (2, 6) and (12, 0)? (a) (3, 7) (b) (14, 6) (c) (5, 3) (d) (7, 3)
19. 19.What is the distance between the points (8, 2) and (13, 14)? (a) 169 (b) 13 (c) 17 (d) 14
20. 20.What is the distance between the points (9, 18) and (14, 6)? (a) 17 (b) 169 (c) 14 (d) 13
21. 21.What is the distance between the points (4, 13) and (10, 5)? (a) 100 (b) 10 (c) 11 (d) 14
22. 22.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
23. 23.What is the distance between the points (5, 15) and (21, 3)? (a) 28 (b) 21 (c) 20 (d) 400
24. 24.What is the distance between the points (6, 16) and (21, 8)? (a) 17 (b) 23 (c) 18 (d) 289
25. 25.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
26. 26.What is the distance between the points (5, 5) and (11, 13)? (a) 10 (b) 14 (c) 11 (d) 100
27. 27.What is the distance between the points (3, 9) and (15, 25)? (a) 21 (b) 20 (c) 28 (d) 400
28. 28.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
29. 29.In which quadrant does the point (4, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
30. 30.What is the midpoint of the line joining (5, 6) and (7, 18)? (a) (12, 24) (b) (1, 6) (c) (12, 6) (d) (6, 12)
31. 31.What is the midpoint of the line joining (0, 7) and (12, 1)? (a) (6, 4) (b) (4, 6) (c) (6, 3) (d) (12, 8)
32. 32.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
33. 33.What is the midpoint of the line joining (1, 7) and (5, 5)? (a) (6, 3) (b) (2, 1) (c) (3, 6) (d) (6, 12)
34. 34.What is the distance between the points (1, 0) and (17, 12)? (a) 28 (b) 20 (c) 21 (d) 400
35. 35.In which quadrant does the point (8, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
36. 36.What is the distance between the points (5, 14) and (17, 5)? (a) 21 (b) 16 (c) 15 (d) 225
37. 37.In which quadrant does the point (5, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
38. 38.In which quadrant does the point (5, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
39. 39.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
40. 40.What is the distance between the points (2, 3) and (18, 15)? (a) 400 (b) 28 (c) 20 (d) 21

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