Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 608 · 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 (5, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
2. 2.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
3. 3.What is the distance between the points (2, 18) and (7, 6)? (a) 17 (b) 14 (c) 169 (d) 13
4. 4.What is the distance between the points (0, 7) and (3, 11)? (a) 5 (b) 6 (c) 25 (d) 7
5. 5.What is the midpoint of the line joining (7, 1) and (17, 3)? (a) (24, 4) (b) (12, 2) (c) (2, 12) (d) (5, 1)
6. 6.What is the distance between the points (0, 10) and (15, 2)? (a) 17 (b) 23 (c) 289 (d) 18
7. 7.In which quadrant does the point (−1, −8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
8. 8.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
9. 9.What is the midpoint of the line joining (1, 12) and (5, 4)? (a) (2, 4) (b) (3, 8) (c) (6, 16) (d) (8, 3)
10. 10.In which quadrant does the point (1, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
11. 11.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
12. 12.In which quadrant does the point (9, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
13. 13.What is the distance between the points (9, 2) and (17, 8)? (a) 11 (b) 10 (c) 100 (d) 14
14. 14.What is the distance between the points (0, 16) and (12, 7)? (a) 21 (b) 16 (c) 225 (d) 15
15. 15.What is the midpoint of the line joining (8, 3) and (18, 5)? (a) (4, 13) (b) (5, 1) (c) (13, 4) (d) (26, 8)
16. 16.What is the midpoint of the line joining (2, 8) and (14, 10)? (a) (9, 8) (b) (16, 18) (c) (6, 1) (d) (8, 9)
17. 17.What is the distance between the points (3, 14) and (27, 7)? (a) 26 (b) 31 (c) 25 (d) 625
18. 18.What is the distance between the points (3, 5) and (6, 1)? (a) 7 (b) 5 (c) 6 (d) 25
19. 19.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
20. 20.What is the midpoint of the line joining (1, 12) and (11, 6)? (a) (12, 18) (b) (9, 6) (c) (6, 9) (d) (5, 3)
21. 21.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
22. 22.What is the midpoint of the line joining (2, 7) and (4, 3)? (a) (5, 3) (b) (1, 2) (c) (3, 5) (d) (6, 10)
23. 23.In which quadrant does the point (6, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
24. 24.What is the distance between the points (9, 0) and (21, 9)? (a) 21 (b) 225 (c) 16 (d) 15
25. 25.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
26. 26.What is the distance between the points (9, 8) and (18, 20)? (a) 16 (b) 15 (c) 21 (d) 225
27. 27.In which quadrant does the point (−9, −7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
28. 28.In which quadrant does the point (−8, 2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
29. 29.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
30. 30.What is the distance between the points (1, 9) and (10, 21)? (a) 15 (b) 21 (c) 225 (d) 16
31. 31.What is the midpoint of the line joining (7, 9) and (19, 19)? (a) (26, 28) (b) (6, 5) (c) (13, 14) (d) (14, 13)
32. 32.What is the distance between the points (8, 1) and (20, 10)? (a) 21 (b) 225 (c) 16 (d) 15
33. 33.What is the midpoint of the line joining (10, 16) and (18, 8)? (a) (28, 24) (b) (4, 4) (c) (12, 14) (d) (14, 12)
34. 34.What is the distance between the points (6, 7) and (13, 31)? (a) 31 (b) 25 (c) 625 (d) 26
35. 35.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
36. 36.In which quadrant does the point (3, −9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
37. 37.What is the midpoint of the line joining (3, 0) and (5, 8)? (a) (1, 4) (b) (8, 8) (c) (4, 4) (d) (5, 4)
38. 38.In which quadrant does the point (−6, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
39. 39.What is the midpoint of the line joining (5, 17) and (17, 5)? (a) (22, 22) (b) (6, 6) (c) (12, 11) (d) (11, 11)
40. 40.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10

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