Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 318 · 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 (−8, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
2. 2.What is the distance between the points (0, 14) and (6, 6)? (a) 10 (b) 100 (c) 14 (d) 11
3. 3.What is the distance between the points (2, 14) and (14, 9)? (a) 14 (b) 169 (c) 13 (d) 17
4. 4.What is the midpoint of the line joining (10, 7) and (14, 1)? (a) (24, 8) (b) (2, 3) (c) (12, 4) (d) (4, 12)
5. 5.In which quadrant does the point (4, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
6. 6.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
7. 7.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
8. 8.In which quadrant does the point (−2, 9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
9. 9.What is the midpoint of the line joining (3, 1) and (5, 9)? (a) (5, 4) (b) (1, 4) (c) (8, 10) (d) (4, 5)
10. 10.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
11. 11.In which quadrant does the point (6, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
12. 12.What is the distance between the points (1, 3) and (13, 19)? (a) 21 (b) 400 (c) 20 (d) 28
13. 13.What is the distance between the points (3, 18) and (8, 6)? (a) 14 (b) 169 (c) 13 (d) 17
14. 14.What is the midpoint of the line joining (9, 10) and (15, 18)? (a) (14, 12) (b) (12, 14) (c) (24, 28) (d) (3, 4)
15. 15.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
16. 16.What is the distance between the points (2, 1) and (26, 8)? (a) 31 (b) 25 (c) 625 (d) 26
17. 17.In which quadrant does the point (7, −2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
18. 18.What is the distance between the points (9, 14) and (21, 5)? (a) 16 (b) 21 (c) 15 (d) 225
19. 19.What is the distance between the points (6, 6) and (15, 18)? (a) 225 (b) 15 (c) 16 (d) 21
20. 20.What is the midpoint of the line joining (0, 2) and (12, 12)? (a) (7, 6) (b) (12, 14) (c) (6, 5) (d) (6, 7)
21. 21.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
22. 22.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 225 (c) 16 (d) 21
23. 23.What is the midpoint of the line joining (5, 6) and (11, 10)? (a) (3, 2) (b) (9, 8) (c) (8, 8) (d) (16, 16)
24. 24.What is the distance between the points (9, 4) and (18, 16)? (a) 16 (b) 225 (c) 21 (d) 15
25. 25.What is the midpoint of the line joining (2, 15) and (6, 3)? (a) (9, 4) (b) (4, 9) (c) (8, 18) (d) (2, 6)
26. 26.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 14 (d) 17
27. 27.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
28. 28.What is the distance between the points (8, 0) and (20, 5)? (a) 17 (b) 169 (c) 14 (d) 13
29. 29.What is the midpoint of the line joining (3, 6) and (5, 8)? (a) (8, 14) (b) (4, 7) (c) (1, 1) (d) (7, 4)
30. 30.In which quadrant does the point (8, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
31. 31.In which quadrant does the point (−5, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
32. 32.In which quadrant does the point (6, 9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
33. 33.What is the distance between the points (0, 5) and (12, 10)? (a) 17 (b) 14 (c) 169 (d) 13
34. 34.What is the distance between the points (3, 8) and (11, 2)? (a) 11 (b) 10 (c) 14 (d) 100
35. 35.What is the distance between the points (0, 8) and (6, 16)? (a) 14 (b) 100 (c) 11 (d) 10
36. 36.What is the distance between the points (0, 3) and (4, 6)? (a) 7 (b) 5 (c) 6 (d) 25
37. 37.What is the midpoint of the line joining (4, 2) and (14, 14)? (a) (8, 9) (b) (9, 8) (c) (18, 16) (d) (5, 6)
38. 38.In which quadrant does the point (−1, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
39. 39.What is the midpoint of the line joining (0, 8) and (6, 20)? (a) (14, 3) (b) (3, 14) (c) (6, 28) (d) (3, 6)
40. 40.What is the midpoint of the line joining (2, 11) and (6, 3)? (a) (2, 4) (b) (8, 14) (c) (7, 4) (d) (4, 7)

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