Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 766 · 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.In which quadrant does the point (9, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
2. 2.What is the distance between the points (1, 21) and (10, 9)? (a) 21 (b) 16 (c) 15 (d) 225
3. 3.What is the distance between the points (9, 5) and (21, 0)? (a) 14 (b) 13 (c) 169 (d) 17
4. 4.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
5. 5.What is the distance between the points (2, 24) and (10, 9)? (a) 18 (b) 23 (c) 17 (d) 289
6. 6.What is the distance between the points (4, 12) and (28, 5)? (a) 25 (b) 625 (c) 31 (d) 26
7. 7.What is the midpoint of the line joining (0, 10) and (4, 0)? (a) (4, 10) (b) (5, 2) (c) (2, 5) (d) (3, 5)
8. 8.What is the distance between the points (1, 14) and (17, 2)? (a) 21 (b) 20 (c) 400 (d) 28
9. 9.In which quadrant does the point (7, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
10. 10.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
11. 11.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
12. 12.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
13. 13.What is the midpoint of the line joining (10, 13) and (22, 3)? (a) (8, 16) (b) (16, 8) (c) (6, 5) (d) (32, 16)
14. 14.What is the midpoint of the line joining (1, 1) and (3, 9)? (a) (4, 10) (b) (1, 4) (c) (5, 2) (d) (2, 5)
15. 15.What is the midpoint of the line joining (5, 12) and (7, 10)? (a) (12, 22) (b) (1, 1) (c) (6, 11) (d) (11, 6)
16. 16.In which quadrant does the point (2, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
17. 17.What is the midpoint of the line joining (5, 6) and (7, 8)? (a) (6, 7) (b) (7, 6) (c) (12, 14) (d) (1, 1)
18. 18.What is the distance between the points (0, 5) and (3, 1)? (a) 6 (b) 7 (c) 5 (d) 25
19. 19.In which quadrant does the point (−7, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
20. 20.In which quadrant does the point (7, 4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
21. 21.What is the distance between the points (2, 9) and (14, 0)? (a) 16 (b) 21 (c) 15 (d) 225
22. 22.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 225 (c) 16 (d) 21
23. 23.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
24. 24.What is the distance between the points (7, 21) and (23, 9)? (a) 20 (b) 28 (c) 21 (d) 400
25. 25.What is the distance between the points (7, 1) and (12, 13)? (a) 169 (b) 13 (c) 14 (d) 17
26. 26.In which quadrant does the point (8, −6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
27. 27.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
28. 28.What is the midpoint of the line joining (0, 14) and (2, 4)? (a) (1, 9) (b) (2, 18) (c) (9, 1) (d) (1, 5)
29. 29.In which quadrant does the point (2, −1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
30. 30.What is the distance between the points (4, 13) and (10, 5)? (a) 11 (b) 14 (c) 10 (d) 100
31. 31.What is the distance between the points (1, 5) and (13, 0)? (a) 13 (b) 14 (c) 17 (d) 169
32. 32.What is the distance between the points (3, 13) and (19, 1)? (a) 400 (b) 20 (c) 28 (d) 21
33. 33.What is the midpoint of the line joining (10, 7) and (14, 19)? (a) (2, 6) (b) (13, 12) (c) (12, 13) (d) (24, 26)
34. 34.What is the midpoint of the line joining (5, 1) and (7, 13)? (a) (12, 14) (b) (7, 6) (c) (1, 6) (d) (6, 7)
35. 35.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
36. 36.In which quadrant does the point (5, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
37. 37.In which quadrant does the point (−4, −7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
38. 38.In which quadrant does the point (3, 6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
39. 39.In which quadrant does the point (−5, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
40. 40.In which quadrant does the point (−3, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant

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