Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 793 · 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 midpoint of the line joining (2, 2) and (10, 10)? (a) (6, 6) (b) (4, 4) (c) (7, 6) (d) (12, 12)
2. 2.What is the distance between the points (0, 9) and (8, 3)? (a) 100 (b) 10 (c) 14 (d) 11
3. 3.In which quadrant does the point (3, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
4. 4.In which quadrant does the point (−2, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
5. 5.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
6. 6.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
7. 7.What is the distance between the points (0, 1) and (16, 13)? (a) 28 (b) 20 (c) 21 (d) 400
8. 8.What is the distance between the points (1, 5) and (25, 12)? (a) 625 (b) 26 (c) 25 (d) 31
9. 9.In which quadrant does the point (3, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
10. 10.What is the distance between the points (8, 4) and (20, 9)? (a) 14 (b) 17 (c) 169 (d) 13
11. 11.What is the distance between the points (8, 5) and (15, 29)? (a) 625 (b) 25 (c) 31 (d) 26
12. 12.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 28 (d) 20
13. 13.What is the midpoint of the line joining (10, 11) and (16, 3)? (a) (26, 14) (b) (3, 4) (c) (7, 13) (d) (13, 7)
14. 14.What is the distance between the points (2, 19) and (7, 7)? (a) 14 (b) 13 (c) 17 (d) 169
15. 15.In which quadrant does the point (7, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
16. 16.What is the distance between the points (2, 2) and (14, 7)? (a) 13 (b) 169 (c) 17 (d) 14
17. 17.What is the distance between the points (6, 18) and (14, 3)? (a) 17 (b) 23 (c) 289 (d) 18
18. 18.What is the distance between the points (1, 4) and (16, 12)? (a) 289 (b) 17 (c) 18 (d) 23
19. 19.What is the midpoint of the line joining (6, 8) and (10, 12)? (a) (2, 2) (b) (8, 10) (c) (10, 8) (d) (16, 20)
20. 20.What is the midpoint of the line joining (5, 12) and (11, 10)? (a) (11, 8) (b) (8, 11) (c) (16, 22) (d) (3, 1)
21. 21.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
22. 22.In which quadrant does the point (−3, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
23. 23.In which quadrant does the point (1, 9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
24. 24.In which quadrant does the point (−4, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
25. 25.What is the midpoint of the line joining (0, 2) and (10, 4)? (a) (5, 3) (b) (5, 1) (c) (3, 5) (d) (10, 6)
26. 26.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
27. 27.In which quadrant does the point (−9, 6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
28. 28.What is the distance between the points (3, 2) and (6, 6)? (a) 7 (b) 25 (c) 6 (d) 5
29. 29.What is the midpoint of the line joining (8, 3) and (12, 5)? (a) (10, 4) (b) (20, 8) (c) (4, 10) (d) (2, 1)
30. 30.What is the distance between the points (3, 9) and (15, 0)? (a) 15 (b) 225 (c) 21 (d) 16
31. 31.In which quadrant does the point (7, 9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
32. 32.What is the distance between the points (9, 16) and (24, 8)? (a) 18 (b) 17 (c) 23 (d) 289
33. 33.What is the midpoint of the line joining (2, 2) and (6, 4)? (a) (4, 3) (b) (2, 1) (c) (3, 4) (d) (8, 6)
34. 34.What is the distance between the points (0, 2) and (12, 7)? (a) 169 (b) 13 (c) 17 (d) 14
35. 35.What is the distance between the points (3, 9) and (12, 21)? (a) 21 (b) 15 (c) 225 (d) 16
36. 36.What is the midpoint of the line joining (1, 4) and (5, 6)? (a) (6, 10) (b) (2, 1) (c) (3, 5) (d) (5, 3)
37. 37.What is the midpoint of the line joining (7, 2) and (19, 12)? (a) (6, 5) (b) (7, 13) (c) (13, 7) (d) (26, 14)
38. 38.In which quadrant does the point (5, −7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
39. 39.What is the midpoint of the line joining (9, 2) and (13, 0)? (a) (2, 1) (b) (11, 1) (c) (1, 11) (d) (22, 2)
40. 40.What is the distance between the points (8, 18) and (24, 6)? (a) 21 (b) 28 (c) 400 (d) 20

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