Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 267 · 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, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
2. 2.What is the midpoint of the line joining (9, 8) and (15, 20)? (a) (24, 28) (b) (12, 14) (c) (3, 6) (d) (14, 12)
3. 3.What is the distance between the points (8, 0) and (11, 4)? (a) 7 (b) 25 (c) 5 (d) 6
4. 4.What is the distance between the points (8, 0) and (16, 6)? (a) 10 (b) 100 (c) 14 (d) 11
5. 5.In which quadrant does the point (8, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
6. 6.What is the distance between the points (3, 17) and (8, 5)? (a) 17 (b) 169 (c) 13 (d) 14
7. 7.In which quadrant does the point (−4, −9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
8. 8.In which quadrant does the point (8, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
9. 9.What is the midpoint of the line joining (2, 5) and (14, 1)? (a) (6, 2) (b) (3, 8) (c) (8, 3) (d) (16, 6)
10. 10.What is the midpoint of the line joining (2, 2) and (10, 6)? (a) (12, 8) (b) (4, 6) (c) (4, 2) (d) (6, 4)
11. 11.What is the distance between the points (6, 8) and (18, 17)? (a) 225 (b) 21 (c) 15 (d) 16
12. 12.What is the midpoint of the line joining (9, 14) and (15, 2)? (a) (3, 6) (b) (8, 12) (c) (24, 16) (d) (12, 8)
13. 13.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
14. 14.In which quadrant does the point (−1, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
15. 15.What is the midpoint of the line joining (7, 0) and (9, 10)? (a) (8, 5) (b) (5, 8) (c) (16, 10) (d) (1, 5)
16. 16.What is the distance between the points (1, 0) and (13, 9)? (a) 15 (b) 225 (c) 21 (d) 16
17. 17.What is the midpoint of the line joining (6, 3) and (12, 1)? (a) (3, 1) (b) (18, 4) (c) (2, 9) (d) (9, 2)
18. 18.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
19. 19.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
20. 20.What is the midpoint of the line joining (7, 6) and (11, 16)? (a) (18, 22) (b) (2, 5) (c) (11, 9) (d) (9, 11)
21. 21.What is the midpoint of the line joining (0, 10) and (10, 20)? (a) (10, 30) (b) (5, 15) (c) (5, 5) (d) (15, 5)
22. 22.What is the midpoint of the line joining (9, 12) and (19, 4)? (a) (5, 4) (b) (14, 8) (c) (8, 14) (d) (28, 16)
23. 23.In which quadrant does the point (−6, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
24. 24.In which quadrant does the point (3, −8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
25. 25.What is the midpoint of the line joining (1, 7) and (7, 9)? (a) (8, 16) (b) (4, 8) (c) (8, 4) (d) (3, 1)
26. 26.In which quadrant does the point (7, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
27. 27.What is the distance between the points (6, 17) and (18, 1)? (a) 28 (b) 21 (c) 20 (d) 400
28. 28.What is the distance between the points (4, 32) and (11, 8)? (a) 625 (b) 31 (c) 26 (d) 25
29. 29.What is the midpoint of the line joining (1, 6) and (9, 8)? (a) (7, 5) (b) (5, 7) (c) (4, 1) (d) (10, 14)
30. 30.What is the distance between the points (1, 12) and (4, 8)? (a) 25 (b) 7 (c) 5 (d) 6
31. 31.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
32. 32.In which quadrant does the point (8, 5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
33. 33.In which quadrant does the point (5, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
34. 34.In which quadrant does the point (4, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
35. 35.What is the midpoint of the line joining (10, 5) and (22, 3)? (a) (16, 4) (b) (6, 1) (c) (4, 16) (d) (32, 8)
36. 36.In which quadrant does the point (6, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
37. 37.What is the distance between the points (9, 9) and (21, 25)? (a) 20 (b) 21 (c) 400 (d) 28
38. 38.What is the distance between the points (7, 16) and (19, 0)? (a) 28 (b) 21 (c) 20 (d) 400
39. 39.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
40. 40.What is the midpoint of the line joining (7, 2) and (13, 10)? (a) (20, 12) (b) (10, 6) (c) (3, 4) (d) (6, 10)

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