Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 939 · 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 (4, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
2. 2.What is the midpoint of the line joining (5, 17) and (17, 5)? (a) (6, 6) (b) (12, 11) (c) (11, 11) (d) (22, 22)
3. 3.What is the distance between the points (0, 14) and (12, 9)? (a) 13 (b) 17 (c) 169 (d) 14
4. 4.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
5. 5.What is the midpoint of the line joining (3, 3) and (7, 13)? (a) (8, 5) (b) (2, 5) (c) (10, 16) (d) (5, 8)
6. 6.In which quadrant does the point (−5, −6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
7. 7.In which quadrant does the point (1, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
8. 8.What is the distance between the points (8, 17) and (24, 5)? (a) 20 (b) 400 (c) 21 (d) 28
9. 9.What is the midpoint of the line joining (5, 14) and (15, 4)? (a) (10, 9) (b) (5, 5) (c) (9, 10) (d) (20, 18)
10. 10.In which quadrant does the point (−8, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
11. 11.In which quadrant does the point (−1, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
12. 12.In which quadrant does the point (−2, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
13. 13.What is the distance between the points (0, 9) and (24, 2)? (a) 625 (b) 25 (c) 31 (d) 26
14. 14.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
15. 15.What is the midpoint of the line joining (4, 3) and (16, 11)? (a) (6, 4) (b) (10, 7) (c) (20, 14) (d) (7, 10)
16. 16.In which quadrant does the point (−1, 4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
17. 17.What is the distance between the points (3, 0) and (8, 12)? (a) 14 (b) 13 (c) 169 (d) 17
18. 18.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
19. 19.What is the distance between the points (3, 2) and (11, 17)? (a) 17 (b) 18 (c) 289 (d) 23
20. 20.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
21. 21.In which quadrant does the point (−8, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
22. 22.What is the distance between the points (6, 9) and (18, 18)? (a) 21 (b) 16 (c) 15 (d) 225
23. 23.What is the distance between the points (3, 11) and (6, 7)? (a) 25 (b) 5 (c) 6 (d) 7
24. 24.What is the midpoint of the line joining (0, 10) and (12, 4)? (a) (12, 14) (b) (6, 7) (c) (6, 3) (d) (7, 6)
25. 25.In which quadrant does the point (2, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
26. 26.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
27. 27.In which quadrant does the point (7, 4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
28. 28.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
29. 29.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
30. 30.What is the midpoint of the line joining (3, 1) and (5, 7)? (a) (1, 3) (b) (8, 8) (c) (4, 4) (d) (5, 4)
31. 31.What is the midpoint of the line joining (6, 4) and (10, 0)? (a) (16, 4) (b) (8, 2) (c) (2, 8) (d) (2, 2)
32. 32.What is the distance between the points (7, 9) and (22, 1)? (a) 18 (b) 289 (c) 17 (d) 23
33. 33.What is the distance between the points (1, 6) and (13, 11)? (a) 17 (b) 13 (c) 14 (d) 169
34. 34.What is the midpoint of the line joining (1, 4) and (11, 12)? (a) (8, 6) (b) (12, 16) (c) (6, 8) (d) (5, 4)
35. 35.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
36. 36.In which quadrant does the point (8, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
37. 37.What is the distance between the points (4, 8) and (28, 1)? (a) 25 (b) 26 (c) 625 (d) 31
38. 38.In which quadrant does the point (1, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
39. 39.What is the distance between the points (0, 14) and (15, 6)? (a) 17 (b) 18 (c) 289 (d) 23
40. 40.What is the midpoint of the line joining (10, 10) and (12, 14)? (a) (11, 12) (b) (12, 11) (c) (1, 2) (d) (22, 24)

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