Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 978 · 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 (−2, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
2. 2.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
3. 3.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
4. 4.In which quadrant does the point (−2, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
5. 5.In which quadrant does the point (−4, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
6. 6.What is the distance between the points (7, 9) and (22, 17)? (a) 289 (b) 23 (c) 17 (d) 18
7. 7.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
8. 8.What is the midpoint of the line joining (0, 8) and (8, 18)? (a) (13, 4) (b) (4, 13) (c) (4, 5) (d) (8, 26)
9. 9.What is the distance between the points (8, 8) and (16, 14)? (a) 11 (b) 100 (c) 10 (d) 14
10. 10.What is the midpoint of the line joining (2, 1) and (8, 3)? (a) (3, 1) (b) (10, 4) (c) (5, 2) (d) (2, 5)
11. 11.What is the midpoint of the line joining (6, 10) and (10, 0)? (a) (16, 10) (b) (5, 8) (c) (8, 5) (d) (2, 5)
12. 12.What is the midpoint of the line joining (3, 16) and (13, 6)? (a) (8, 11) (b) (11, 8) (c) (5, 5) (d) (16, 22)
13. 13.What is the midpoint of the line joining (9, 2) and (11, 6)? (a) (1, 2) (b) (20, 8) (c) (4, 10) (d) (10, 4)
14. 14.What is the distance between the points (9, 2) and (18, 14)? (a) 16 (b) 21 (c) 15 (d) 225
15. 15.In which quadrant does the point (1, −8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
16. 16.In which quadrant does the point (−7, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
17. 17.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
18. 18.In which quadrant does the point (−1, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
19. 19.What is the distance between the points (6, 3) and (21, 11)? (a) 17 (b) 23 (c) 18 (d) 289
20. 20.What is the distance between the points (7, 25) and (14, 1)? (a) 625 (b) 26 (c) 25 (d) 31
21. 21.What is the midpoint of the line joining (3, 3) and (7, 13)? (a) (5, 8) (b) (8, 5) (c) (2, 5) (d) (10, 16)
22. 22.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
23. 23.In which quadrant does the point (−2, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
24. 24.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
25. 25.What is the distance between the points (0, 13) and (5, 1)? (a) 17 (b) 13 (c) 14 (d) 169
26. 26.What is the midpoint of the line joining (5, 10) and (15, 12)? (a) (10, 11) (b) (11, 10) (c) (20, 22) (d) (5, 1)
27. 27.What is the distance between the points (7, 17) and (13, 9)? (a) 10 (b) 11 (c) 14 (d) 100
28. 28.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
29. 29.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
30. 30.What is the distance between the points (1, 4) and (4, 8)? (a) 7 (b) 5 (c) 6 (d) 25
31. 31.What is the distance between the points (9, 16) and (21, 0)? (a) 400 (b) 21 (c) 20 (d) 28
32. 32.In which quadrant does the point (−1, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
33. 33.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
34. 34.What is the midpoint of the line joining (0, 10) and (2, 18)? (a) (14, 1) (b) (1, 4) (c) (1, 14) (d) (2, 28)
35. 35.What is the midpoint of the line joining (1, 10) and (9, 16)? (a) (13, 5) (b) (5, 13) (c) (4, 3) (d) (10, 26)
36. 36.What is the midpoint of the line joining (7, 14) and (9, 10)? (a) (1, 2) (b) (16, 24) (c) (12, 8) (d) (8, 12)
37. 37.What is the midpoint of the line joining (4, 1) and (12, 13)? (a) (16, 14) (b) (8, 7) (c) (4, 6) (d) (7, 8)
38. 38.What is the midpoint of the line joining (5, 12) and (15, 10)? (a) (5, 1) (b) (11, 10) (c) (10, 11) (d) (20, 22)
39. 39.In which quadrant does the point (−3, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
40. 40.In which quadrant does the point (4, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant

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