Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 246 · 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 (1, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
2. 2.What is the midpoint of the line joining (10, 1) and (22, 7)? (a) (32, 8) (b) (6, 3) (c) (16, 4) (d) (4, 16)
3. 3.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
4. 4.What is the midpoint of the line joining (7, 8) and (19, 10)? (a) (9, 13) (b) (6, 1) (c) (26, 18) (d) (13, 9)
5. 5.In which quadrant does the point (9, −7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
6. 6.What is the midpoint of the line joining (8, 3) and (18, 15)? (a) (5, 6) (b) (26, 18) (c) (9, 13) (d) (13, 9)
7. 7.What is the distance between the points (6, 1) and (18, 6)? (a) 169 (b) 14 (c) 13 (d) 17
8. 8.What is the midpoint of the line joining (3, 11) and (9, 7)? (a) (3, 2) (b) (6, 9) (c) (9, 6) (d) (12, 18)
9. 9.What is the midpoint of the line joining (7, 9) and (9, 19)? (a) (16, 28) (b) (1, 5) (c) (14, 8) (d) (8, 14)
10. 10.What is the distance between the points (5, 2) and (17, 7)? (a) 14 (b) 169 (c) 13 (d) 17
11. 11.In which quadrant does the point (−1, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
12. 12.What is the midpoint of the line joining (9, 10) and (11, 4)? (a) (1, 3) (b) (7, 10) (c) (20, 14) (d) (10, 7)
13. 13.In which quadrant does the point (−7, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
14. 14.What is the distance between the points (8, 4) and (20, 13)? (a) 21 (b) 225 (c) 16 (d) 15
15. 15.In which quadrant does the point (2, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
16. 16.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
17. 17.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
18. 18.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
19. 19.What is the midpoint of the line joining (10, 13) and (16, 5)? (a) (26, 18) (b) (9, 13) (c) (13, 9) (d) (3, 4)
20. 20.What is the midpoint of the line joining (7, 6) and (11, 0)? (a) (2, 3) (b) (9, 3) (c) (18, 6) (d) (3, 9)
21. 21.What is the distance between the points (7, 18) and (16, 6)? (a) 15 (b) 21 (c) 225 (d) 16
22. 22.What is the distance between the points (8, 20) and (20, 4)? (a) 21 (b) 20 (c) 28 (d) 400
23. 23.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
24. 24.In which quadrant does the point (9, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
25. 25.What is the distance between the points (0, 5) and (9, 17)? (a) 225 (b) 16 (c) 21 (d) 15
26. 26.In which quadrant does the point (9, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
27. 27.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
28. 28.In which quadrant does the point (−5, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
29. 29.In which quadrant does the point (4, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
30. 30.What is the distance between the points (1, 1) and (16, 9)? (a) 289 (b) 23 (c) 17 (d) 18
31. 31.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
32. 32.What is the midpoint of the line joining (6, 9) and (14, 7)? (a) (4, 1) (b) (20, 16) (c) (10, 8) (d) (8, 10)
33. 33.In which quadrant does the point (−1, 4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
34. 34.In which quadrant does the point (4, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
35. 35.In which quadrant does the point (1, −4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
36. 36.What is the distance between the points (2, 9) and (9, 33)? (a) 25 (b) 31 (c) 625 (d) 26
37. 37.What is the midpoint of the line joining (2, 6) and (4, 18)? (a) (1, 6) (b) (6, 24) (c) (12, 3) (d) (3, 12)
38. 38.What is the midpoint of the line joining (0, 10) and (4, 22)? (a) (2, 6) (b) (2, 16) (c) (4, 32) (d) (16, 2)
39. 39.What is the distance between the points (0, 10) and (4, 7)? (a) 5 (b) 7 (c) 25 (d) 6
40. 40.What is the midpoint of the line joining (8, 3) and (20, 9)? (a) (28, 12) (b) (6, 3) (c) (14, 6) (d) (6, 14)

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