Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 506 · 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.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
2. 2.In which quadrant does the point (2, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
3. 3.What is the distance between the points (9, 28) and (16, 4)? (a) 25 (b) 625 (c) 26 (d) 31
4. 4.What is the distance between the points (3, 7) and (19, 19)? (a) 28 (b) 21 (c) 400 (d) 20
5. 5.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
6. 6.In which quadrant does the point (−5, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
7. 7.What is the midpoint of the line joining (5, 17) and (7, 7)? (a) (12, 24) (b) (12, 6) (c) (1, 5) (d) (6, 12)
8. 8.What is the midpoint of the line joining (5, 11) and (7, 9)? (a) (1, 1) (b) (12, 20) (c) (10, 6) (d) (6, 10)
9. 9.What is the distance between the points (5, 21) and (10, 9)? (a) 17 (b) 169 (c) 14 (d) 13
10. 10.What is the distance between the points (4, 13) and (16, 4)? (a) 21 (b) 16 (c) 15 (d) 225
11. 11.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
12. 12.In which quadrant does the point (6, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
13. 13.What is the distance between the points (2, 0) and (6, 3)? (a) 7 (b) 5 (c) 25 (d) 6
14. 14.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
15. 15.In which quadrant does the point (2, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
16. 16.In which quadrant does the point (6, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
17. 17.In which quadrant does the point (7, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
18. 18.In which quadrant does the point (−2, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
19. 19.What is the midpoint of the line joining (6, 20) and (14, 8)? (a) (4, 6) (b) (10, 14) (c) (14, 10) (d) (20, 28)
20. 20.What is the midpoint of the line joining (1, 10) and (3, 0)? (a) (5, 2) (b) (1, 5) (c) (4, 10) (d) (2, 5)
21. 21.What is the distance between the points (4, 8) and (8, 5)? (a) 7 (b) 6 (c) 5 (d) 25
22. 22.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
23. 23.In which quadrant does the point (8, −4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
24. 24.In which quadrant does the point (2, 2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
25. 25.What is the distance between the points (1, 3) and (17, 15)? (a) 400 (b) 20 (c) 21 (d) 28
26. 26.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 13 (d) 17
27. 27.In which quadrant does the point (4, 7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
28. 28.What is the midpoint of the line joining (8, 0) and (14, 4)? (a) (3, 2) (b) (22, 4) (c) (2, 11) (d) (11, 2)
29. 29.What is the distance between the points (3, 22) and (15, 6)? (a) 20 (b) 21 (c) 28 (d) 400
30. 30.What is the midpoint of the line joining (0, 5) and (4, 17)? (a) (4, 22) (b) (11, 2) (c) (2, 11) (d) (2, 6)
31. 31.In which quadrant does the point (−5, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
32. 32.What is the midpoint of the line joining (5, 6) and (17, 2)? (a) (4, 11) (b) (11, 4) (c) (22, 8) (d) (6, 2)
33. 33.What is the distance between the points (9, 12) and (14, 0)? (a) 17 (b) 169 (c) 13 (d) 14
34. 34.In which quadrant does the point (9, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
35. 35.What is the distance between the points (1, 13) and (7, 5)? (a) 11 (b) 100 (c) 10 (d) 14
36. 36.What is the midpoint of the line joining (7, 7) and (17, 11)? (a) (24, 18) (b) (5, 2) (c) (9, 12) (d) (12, 9)
37. 37.What is the distance between the points (5, 8) and (17, 24)? (a) 400 (b) 20 (c) 28 (d) 21
38. 38.What is the distance between the points (2, 6) and (5, 2)? (a) 25 (b) 5 (c) 6 (d) 7
39. 39.What is the distance between the points (4, 11) and (16, 2)? (a) 15 (b) 16 (c) 21 (d) 225
40. 40.What is the midpoint of the line joining (7, 5) and (15, 13)? (a) (9, 11) (b) (22, 18) (c) (11, 9) (d) (4, 4)

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