Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 101 · 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 distance between the points (4, 4) and (13, 16)? (a) 21 (b) 16 (c) 225 (d) 15
2. 2.What is the distance between the points (1, 8) and (9, 2)? (a) 100 (b) 11 (c) 10 (d) 14
3. 3.What is the midpoint of the line joining (3, 14) and (9, 6)? (a) (6, 10) (b) (12, 20) (c) (3, 4) (d) (10, 6)
4. 4.What is the distance between the points (7, 3) and (16, 15)? (a) 21 (b) 15 (c) 225 (d) 16
5. 5.In which quadrant does the point (−8, −9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
6. 6.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
7. 7.What is the midpoint of the line joining (3, 2) and (5, 6)? (a) (1, 2) (b) (5, 4) (c) (4, 4) (d) (8, 8)
8. 8.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
9. 9.In which quadrant does the point (−7, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
10. 10.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
11. 11.In which quadrant does the point (5, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
12. 12.In which quadrant does the point (9, −6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
13. 13.What is the midpoint of the line joining (7, 11) and (19, 9)? (a) (26, 20) (b) (10, 13) (c) (13, 10) (d) (6, 1)
14. 14.What is the distance between the points (3, 3) and (12, 15)? (a) 16 (b) 225 (c) 21 (d) 15
15. 15.In which quadrant does the point (−3, −8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
16. 16.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
17. 17.In which quadrant does the point (−7, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
18. 18.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
19. 19.What is the distance between the points (4, 2) and (9, 14)? (a) 13 (b) 169 (c) 17 (d) 14
20. 20.In which quadrant does the point (1, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
21. 21.In which quadrant does the point (3, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
22. 22.What is the distance between the points (1, 9) and (9, 15)? (a) 10 (b) 11 (c) 100 (d) 14
23. 23.What is the distance between the points (4, 2) and (16, 7)? (a) 17 (b) 13 (c) 14 (d) 169
24. 24.What is the midpoint of the line joining (0, 10) and (2, 4)? (a) (7, 1) (b) (1, 7) (c) (2, 14) (d) (1, 3)
25. 25.In which quadrant does the point (5, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
26. 26.In which quadrant does the point (1, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
27. 27.What is the distance between the points (2, 5) and (11, 17)? (a) 16 (b) 21 (c) 225 (d) 15
28. 28.In which quadrant does the point (9, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
29. 29.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
30. 30.In which quadrant does the point (−5, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
31. 31.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
32. 32.What is the distance between the points (3, 4) and (15, 9)? (a) 13 (b) 17 (c) 169 (d) 14
33. 33.What is the distance between the points (4, 4) and (9, 16)? (a) 169 (b) 14 (c) 13 (d) 17
34. 34.What is the midpoint of the line joining (6, 6) and (8, 4)? (a) (7, 5) (b) (5, 7) (c) (14, 10) (d) (1, 1)
35. 35.What is the midpoint of the line joining (6, 2) and (18, 12)? (a) (24, 14) (b) (6, 5) (c) (7, 12) (d) (12, 7)
36. 36.What is the distance between the points (9, 15) and (15, 7)? (a) 100 (b) 11 (c) 10 (d) 14
37. 37.What is the distance between the points (0, 0) and (5, 12)? (a) 14 (b) 13 (c) 169 (d) 17
38. 38.What is the distance between the points (2, 9) and (10, 3)? (a) 14 (b) 10 (c) 100 (d) 11
39. 39.What is the midpoint of the line joining (8, 11) and (14, 1)? (a) (6, 11) (b) (3, 5) (c) (11, 6) (d) (22, 12)
40. 40.What is the midpoint of the line joining (3, 1) and (11, 7)? (a) (4, 7) (b) (7, 4) (c) (14, 8) (d) (4, 3)

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