Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 540 · 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 (0, 6) and (4, 9)? (a) 5 (b) 6 (c) 25 (d) 7
2. 2.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
3. 3.What is the distance between the points (1, 7) and (10, 19)? (a) 15 (b) 21 (c) 225 (d) 16
4. 4.In which quadrant does the point (9, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
5. 5.In which quadrant does the point (5, 1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
6. 6.What is the midpoint of the line joining (9, 0) and (17, 2)? (a) (1, 13) (b) (13, 1) (c) (4, 1) (d) (26, 2)
7. 7.What is the distance between the points (3, 24) and (10, 0)? (a) 625 (b) 25 (c) 26 (d) 31
8. 8.In which quadrant does the point (7, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
9. 9.In which quadrant does the point (−4, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
10. 10.In which quadrant does the point (−8, −3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
11. 11.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
12. 12.In which quadrant does the point (1, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
13. 13.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
14. 14.What is the midpoint of the line joining (2, 9) and (10, 1)? (a) (4, 4) (b) (6, 5) (c) (5, 6) (d) (12, 10)
15. 15.What is the distance between the points (3, 5) and (12, 17)? (a) 21 (b) 16 (c) 15 (d) 225
16. 16.What is the distance between the points (2, 7) and (18, 19)? (a) 400 (b) 20 (c) 28 (d) 21
17. 17.What is the distance between the points (4, 9) and (28, 2)? (a) 625 (b) 31 (c) 25 (d) 26
18. 18.What is the midpoint of the line joining (10, 6) and (18, 12)? (a) (9, 14) (b) (28, 18) (c) (4, 3) (d) (14, 9)
19. 19.What is the distance between the points (1, 5) and (13, 21)? (a) 400 (b) 28 (c) 21 (d) 20
20. 20.What is the midpoint of the line joining (6, 8) and (8, 14)? (a) (14, 22) (b) (7, 11) (c) (11, 7) (d) (1, 3)
21. 21.In which quadrant does the point (5, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
22. 22.In which quadrant does the point (−6, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
23. 23.In which quadrant does the point (1, −8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
24. 24.In which quadrant does the point (−5, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
25. 25.In which quadrant does the point (1, −6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
26. 26.In which quadrant does the point (−6, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
27. 27.What is the midpoint of the line joining (1, 10) and (13, 6)? (a) (7, 8) (b) (8, 7) (c) (14, 16) (d) (6, 2)
28. 28.What is the distance between the points (7, 5) and (31, 12)? (a) 26 (b) 31 (c) 625 (d) 25
29. 29.What is the distance between the points (9, 16) and (24, 8)? (a) 18 (b) 23 (c) 17 (d) 289
30. 30.In which quadrant does the point (7, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
31. 31.What is the midpoint of the line joining (2, 9) and (14, 3)? (a) (6, 8) (b) (6, 3) (c) (16, 12) (d) (8, 6)
32. 32.In which quadrant does the point (−4, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
33. 33.In which quadrant does the point (−2, 1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
34. 34.What is the midpoint of the line joining (2, 5) and (10, 3)? (a) (4, 6) (b) (4, 1) (c) (6, 4) (d) (12, 8)
35. 35.What is the midpoint of the line joining (4, 8) and (14, 6)? (a) (7, 9) (b) (9, 7) (c) (5, 1) (d) (18, 14)
36. 36.What is the distance between the points (3, 3) and (11, 18)? (a) 289 (b) 23 (c) 17 (d) 18
37. 37.In which quadrant does the point (8, −8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
38. 38.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
39. 39.What is the midpoint of the line joining (5, 2) and (15, 10)? (a) (6, 10) (b) (5, 4) (c) (20, 12) (d) (10, 6)
40. 40.What is the midpoint of the line joining (3, 8) and (13, 14)? (a) (5, 3) (b) (11, 8) (c) (8, 11) (d) (16, 22)

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