Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 813 · 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 (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
2. 2.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
3. 3.In which quadrant does the point (6, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
4. 4.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
5. 5.What is the distance between the points (0, 21) and (5, 9)? (a) 14 (b) 13 (c) 169 (d) 17
6. 6.What is the distance between the points (8, 10) and (32, 3)? (a) 25 (b) 31 (c) 26 (d) 625
7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
8. 8.What is the midpoint of the line joining (9, 3) and (15, 13)? (a) (8, 12) (b) (3, 5) (c) (12, 8) (d) (24, 16)
9. 9.What is the distance between the points (6, 6) and (11, 18)? (a) 14 (b) 17 (c) 13 (d) 169
10. 10.In which quadrant does the point (3, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
11. 11.What is the distance between the points (8, 16) and (14, 8)? (a) 11 (b) 14 (c) 10 (d) 100
12. 12.What is the midpoint of the line joining (3, 0) and (9, 10)? (a) (3, 5) (b) (12, 10) (c) (6, 5) (d) (5, 6)
13. 13.What is the distance between the points (6, 8) and (14, 2)? (a) 100 (b) 10 (c) 14 (d) 11
14. 14.What is the distance between the points (6, 8) and (22, 20)? (a) 21 (b) 400 (c) 28 (d) 20
15. 15.In which quadrant does the point (−1, 8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
16. 16.What is the distance between the points (4, 13) and (9, 1)? (a) 14 (b) 169 (c) 17 (d) 13
17. 17.What is the midpoint of the line joining (9, 6) and (17, 8)? (a) (7, 13) (b) (4, 1) (c) (26, 14) (d) (13, 7)
18. 18.What is the midpoint of the line joining (3, 4) and (11, 0)? (a) (7, 2) (b) (4, 2) (c) (14, 4) (d) (2, 7)
19. 19.What is the distance between the points (7, 11) and (31, 4)? (a) 25 (b) 31 (c) 26 (d) 625
20. 20.What is the midpoint of the line joining (2, 6) and (4, 16)? (a) (3, 11) (b) (11, 3) (c) (6, 22) (d) (1, 5)
21. 21.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
22. 22.What is the midpoint of the line joining (8, 2) and (18, 14)? (a) (13, 8) (b) (26, 16) (c) (5, 6) (d) (8, 13)
23. 23.In which quadrant does the point (−2, 3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
24. 24.What is the distance between the points (6, 13) and (18, 8)? (a) 14 (b) 13 (c) 17 (d) 169
25. 25.What is the distance between the points (5, 24) and (12, 0)? (a) 26 (b) 625 (c) 31 (d) 25
26. 26.What is the midpoint of the line joining (10, 2) and (12, 4)? (a) (1, 1) (b) (11, 3) (c) (3, 11) (d) (22, 6)
27. 27.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
28. 28.What is the distance between the points (3, 7) and (6, 11)? (a) 5 (b) 7 (c) 6 (d) 25
29. 29.What is the distance between the points (2, 14) and (7, 2)? (a) 169 (b) 14 (c) 13 (d) 17
30. 30.What is the distance between the points (8, 18) and (13, 6)? (a) 17 (b) 169 (c) 13 (d) 14
31. 31.What is the distance between the points (1, 15) and (9, 0)? (a) 18 (b) 289 (c) 17 (d) 23
32. 32.In which quadrant does the point (−5, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
33. 33.What is the midpoint of the line joining (2, 15) and (8, 7)? (a) (11, 5) (b) (3, 4) (c) (10, 22) (d) (5, 11)
34. 34.What is the midpoint of the line joining (3, 6) and (7, 12)? (a) (2, 3) (b) (10, 18) (c) (9, 5) (d) (5, 9)
35. 35.In which quadrant does the point (9, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
36. 36.What is the midpoint of the line joining (8, 8) and (18, 4)? (a) (13, 6) (b) (5, 2) (c) (6, 13) (d) (26, 12)
37. 37.In which quadrant does the point (9, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
38. 38.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
39. 39.What is the distance between the points (7, 6) and (31, 13)? (a) 625 (b) 25 (c) 26 (d) 31
40. 40.In which quadrant does the point (−5, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant

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