Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 253 · 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 (2, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
2. 2.What is the midpoint of the line joining (1, 10) and (5, 14)? (a) (2, 2) (b) (12, 3) (c) (3, 12) (d) (6, 24)
3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
4. 4.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 14 (d) 17
5. 5.What is the midpoint of the line joining (2, 7) and (8, 9)? (a) (3, 1) (b) (5, 8) (c) (10, 16) (d) (8, 5)
6. 6.What is the midpoint of the line joining (0, 7) and (8, 3)? (a) (4, 5) (b) (4, 2) (c) (8, 10) (d) (5, 4)
7. 7.In which quadrant does the point (−4, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
8. 8.In which quadrant does the point (−1, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
9. 9.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
10. 10.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
11. 11.What is the distance between the points (9, 4) and (13, 7)? (a) 6 (b) 25 (c) 5 (d) 7
12. 12.What is the midpoint of the line joining (1, 4) and (3, 0)? (a) (1, 2) (b) (2, 2) (c) (3, 2) (d) (4, 4)
13. 13.What is the distance between the points (6, 16) and (30, 9)? (a) 25 (b) 625 (c) 26 (d) 31
14. 14.What is the distance between the points (5, 18) and (21, 6)? (a) 20 (b) 28 (c) 400 (d) 21
15. 15.In which quadrant does the point (1, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
16. 16.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
17. 17.What is the distance between the points (0, 6) and (9, 18)? (a) 16 (b) 225 (c) 15 (d) 21
18. 18.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
19. 19.What is the midpoint of the line joining (7, 5) and (9, 11)? (a) (9, 8) (b) (1, 3) (c) (16, 16) (d) (8, 8)
20. 20.In which quadrant does the point (−6, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
21. 21.What is the distance between the points (6, 19) and (11, 7)? (a) 169 (b) 13 (c) 14 (d) 17
22. 22.What is the midpoint of the line joining (3, 13) and (9, 9)? (a) (12, 22) (b) (6, 11) (c) (3, 2) (d) (11, 6)
23. 23.What is the distance between the points (2, 7) and (7, 19)? (a) 169 (b) 13 (c) 14 (d) 17
24. 24.What is the distance between the points (8, 1) and (13, 13)? (a) 14 (b) 17 (c) 13 (d) 169
25. 25.In which quadrant does the point (−1, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
26. 26.What is the distance between the points (1, 4) and (9, 19)? (a) 17 (b) 18 (c) 289 (d) 23
27. 27.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
28. 28.What is the midpoint of the line joining (0, 7) and (4, 11)? (a) (9, 2) (b) (2, 2) (c) (4, 18) (d) (2, 9)
29. 29.What is the midpoint of the line joining (2, 6) and (4, 10)? (a) (8, 3) (b) (1, 2) (c) (6, 16) (d) (3, 8)
30. 30.What is the midpoint of the line joining (3, 5) and (7, 17)? (a) (2, 6) (b) (11, 5) (c) (5, 11) (d) (10, 22)
31. 31.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
32. 32.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
33. 33.What is the midpoint of the line joining (0, 4) and (6, 6)? (a) (5, 3) (b) (3, 1) (c) (6, 10) (d) (3, 5)
34. 34.What is the distance between the points (1, 20) and (17, 8)? (a) 400 (b) 20 (c) 28 (d) 21
35. 35.In which quadrant does the point (−1, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
36. 36.What is the midpoint of the line joining (0, 8) and (12, 2)? (a) (6, 5) (b) (6, 3) (c) (12, 10) (d) (5, 6)
37. 37.What is the distance between the points (7, 9) and (12, 21)? (a) 14 (b) 169 (c) 13 (d) 17
38. 38.What is the distance between the points (8, 8) and (16, 14)? (a) 100 (b) 11 (c) 14 (d) 10
39. 39.What is the distance between the points (5, 15) and (17, 6)? (a) 225 (b) 16 (c) 21 (d) 15
40. 40.What is the distance between the points (0, 0) and (16, 12)? (a) 21 (b) 28 (c) 20 (d) 400

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