Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 421 · 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 (8, 7) and (10, 11)? (a) (10, 9) (b) (18, 18) (c) (9, 9) (d) (1, 2)
2. 2.In which quadrant does the point (2, −1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
3. 3.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
4. 4.In which quadrant does the point (7, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
5. 5.In which quadrant does the point (−7, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
6. 6.In which quadrant does the point (7, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
7. 7.What is the midpoint of the line joining (2, 7) and (6, 5)? (a) (2, 1) (b) (4, 6) (c) (6, 4) (d) (8, 12)
8. 8.What is the distance between the points (8, 5) and (11, 9)? (a) 25 (b) 7 (c) 6 (d) 5
9. 9.What is the midpoint of the line joining (0, 5) and (12, 3)? (a) (4, 6) (b) (6, 4) (c) (12, 8) (d) (6, 1)
10. 10.What is the midpoint of the line joining (5, 22) and (11, 10)? (a) (16, 32) (b) (3, 6) (c) (8, 16) (d) (16, 8)
11. 11.What is the distance between the points (0, 2) and (4, 5)? (a) 7 (b) 5 (c) 25 (d) 6
12. 12.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
13. 13.What is the distance between the points (9, 10) and (15, 2)? (a) 11 (b) 100 (c) 10 (d) 14
14. 14.What is the midpoint of the line joining (10, 6) and (16, 16)? (a) (11, 13) (b) (26, 22) (c) (3, 5) (d) (13, 11)
15. 15.What is the midpoint of the line joining (0, 7) and (6, 5)? (a) (6, 3) (b) (3, 6) (c) (3, 1) (d) (6, 12)
16. 16.In which quadrant does the point (6, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
17. 17.What is the distance between the points (6, 2) and (18, 18)? (a) 28 (b) 21 (c) 20 (d) 400
18. 18.What is the midpoint of the line joining (5, 0) and (9, 12)? (a) (14, 12) (b) (7, 6) (c) (6, 7) (d) (2, 6)
19. 19.What is the distance between the points (4, 0) and (7, 4)? (a) 5 (b) 25 (c) 6 (d) 7
20. 20.What is the midpoint of the line joining (0, 12) and (2, 10)? (a) (1, 1) (b) (1, 11) (c) (11, 1) (d) (2, 22)
21. 21.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
22. 22.In which quadrant does the point (−2, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
23. 23.In which quadrant does the point (−4, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
24. 24.What is the distance between the points (1, 13) and (6, 1)? (a) 14 (b) 13 (c) 17 (d) 169
25. 25.In which quadrant does the point (6, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
26. 26.What is the distance between the points (7, 16) and (13, 8)? (a) 14 (b) 10 (c) 100 (d) 11
27. 27.In which quadrant does the point (3, −7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
28. 28.What is the midpoint of the line joining (3, 11) and (15, 3)? (a) (7, 9) (b) (18, 14) (c) (9, 7) (d) (6, 4)
29. 29.What is the distance between the points (4, 6) and (8, 3)? (a) 25 (b) 6 (c) 5 (d) 7
30. 30.What is the distance between the points (7, 17) and (12, 5)? (a) 169 (b) 14 (c) 13 (d) 17
31. 31.In which quadrant does the point (8, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
32. 32.What is the midpoint of the line joining (3, 19) and (7, 9)? (a) (10, 28) (b) (2, 5) (c) (14, 5) (d) (5, 14)
33. 33.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
34. 34.What is the midpoint of the line joining (8, 15) and (10, 7)? (a) (9, 11) (b) (18, 22) (c) (1, 4) (d) (11, 9)
35. 35.What is the midpoint of the line joining (1, 8) and (9, 12)? (a) (4, 2) (b) (5, 10) (c) (10, 20) (d) (10, 5)
36. 36.In which quadrant does the point (5, 5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
37. 37.What is the distance between the points (8, 10) and (11, 6)? (a) 6 (b) 25 (c) 5 (d) 7
38. 38.In which quadrant does the point (5, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
39. 39.What is the distance between the points (0, 19) and (12, 3)? (a) 400 (b) 28 (c) 21 (d) 20
40. 40.What is the midpoint of the line joining (5, 6) and (17, 2)? (a) (6, 2) (b) (11, 4) (c) (4, 11) (d) (22, 8)

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