Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 848 · 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.What is the distance between the points (3, 4) and (18, 12)? (a) 289 (b) 17 (c) 23 (d) 18
2. 2.What is the midpoint of the line joining (10, 5) and (18, 3)? (a) (28, 8) (b) (14, 4) (c) (4, 14) (d) (4, 1)
3. 3.What is the distance between the points (0, 0) and (12, 16)? (a) 28 (b) 400 (c) 20 (d) 21
4. 4.What is the distance between the points (5, 13) and (17, 8)? (a) 169 (b) 14 (c) 13 (d) 17
5. 5.What is the distance between the points (0, 5) and (3, 9)? (a) 7 (b) 25 (c) 5 (d) 6
6. 6.In which quadrant does the point (3, 3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
7. 7.What is the distance between the points (8, 4) and (15, 28)? (a) 26 (b) 625 (c) 31 (d) 25
8. 8.What is the midpoint of the line joining (2, 15) and (10, 9)? (a) (6, 12) (b) (4, 3) (c) (12, 6) (d) (12, 24)
9. 9.What is the distance between the points (4, 3) and (8, 6)? (a) 7 (b) 25 (c) 6 (d) 5
10. 10.In which quadrant does the point (2, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
11. 11.What is the distance between the points (5, 4) and (11, 12)? (a) 100 (b) 11 (c) 10 (d) 14
12. 12.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
13. 13.In which quadrant does the point (−3, −7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
14. 14.In which quadrant does the point (−1, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
15. 15.What is the midpoint of the line joining (6, 2) and (8, 10)? (a) (6, 7) (b) (1, 4) (c) (14, 12) (d) (7, 6)
16. 16.What is the distance between the points (8, 12) and (13, 0)? (a) 169 (b) 17 (c) 14 (d) 13
17. 17.What is the distance between the points (2, 1) and (7, 13)? (a) 13 (b) 14 (c) 17 (d) 169
18. 18.What is the midpoint of the line joining (9, 3) and (21, 15)? (a) (6, 6) (b) (30, 18) (c) (15, 9) (d) (9, 15)
19. 19.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
20. 20.In which quadrant does the point (−3, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
21. 21.In which quadrant does the point (5, −3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
22. 22.What is the distance between the points (3, 4) and (8, 16)? (a) 14 (b) 169 (c) 13 (d) 17
23. 23.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
24. 24.What is the distance between the points (2, 33) and (9, 9)? (a) 31 (b) 26 (c) 25 (d) 625
25. 25.What is the distance between the points (4, 11) and (12, 5)? (a) 14 (b) 11 (c) 100 (d) 10
26. 26.In which quadrant does the point (−6, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
27. 27.What is the midpoint of the line joining (5, 18) and (13, 10)? (a) (4, 4) (b) (18, 28) (c) (9, 14) (d) (14, 9)
28. 28.In which quadrant does the point (3, 8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
29. 29.In which quadrant does the point (8, −3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
30. 30.What is the midpoint of the line joining (5, 14) and (13, 6)? (a) (10, 9) (b) (9, 10) (c) (18, 20) (d) (4, 4)
31. 31.In which quadrant does the point (−2, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
32. 32.What is the distance between the points (4, 3) and (10, 11)? (a) 100 (b) 11 (c) 14 (d) 10
33. 33.In which quadrant does the point (1, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
34. 34.In which quadrant does the point (7, 2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
35. 35.What is the distance between the points (4, 31) and (11, 7)? (a) 31 (b) 625 (c) 26 (d) 25
36. 36.What is the midpoint of the line joining (10, 7) and (20, 9)? (a) (5, 1) (b) (15, 8) (c) (30, 16) (d) (8, 15)
37. 37.What is the midpoint of the line joining (8, 18) and (16, 6)? (a) (12, 12) (b) (13, 12) (c) (24, 24) (d) (4, 6)
38. 38.What is the distance between the points (2, 7) and (9, 31)? (a) 26 (b) 31 (c) 625 (d) 25
39. 39.What is the midpoint of the line joining (8, 16) and (10, 10)? (a) (1, 3) (b) (9, 13) (c) (13, 9) (d) (18, 26)
40. 40.What is the distance between the points (1, 8) and (7, 16)? (a) 11 (b) 10 (c) 14 (d) 100

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