Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 234 · 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, 7) and (8, 10)? (a) 5 (b) 6 (c) 25 (d) 7
2. 2.What is the distance between the points (1, 2) and (7, 10)? (a) 100 (b) 10 (c) 14 (d) 11
3. 3.In which quadrant does the point (5, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
4. 4.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
5. 5.What is the midpoint of the line joining (8, 6) and (20, 8)? (a) (14, 7) (b) (7, 14) (c) (6, 1) (d) (28, 14)
6. 6.What is the midpoint of the line joining (2, 11) and (6, 5)? (a) (4, 8) (b) (2, 3) (c) (8, 4) (d) (8, 16)
7. 7.What is the midpoint of the line joining (5, 2) and (9, 0)? (a) (2, 1) (b) (7, 1) (c) (14, 2) (d) (1, 7)
8. 8.What is the distance between the points (3, 9) and (11, 24)? (a) 289 (b) 18 (c) 17 (d) 23
9. 9.What is the distance between the points (3, 7) and (7, 10)? (a) 7 (b) 6 (c) 25 (d) 5
10. 10.What is the distance between the points (3, 15) and (19, 3)? (a) 400 (b) 28 (c) 21 (d) 20
11. 11.What is the midpoint of the line joining (10, 10) and (20, 14)? (a) (5, 2) (b) (30, 24) (c) (12, 15) (d) (15, 12)
12. 12.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
13. 13.What is the distance between the points (5, 5) and (17, 14)? (a) 21 (b) 15 (c) 225 (d) 16
14. 14.In which quadrant does the point (−3, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
15. 15.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
16. 16.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
17. 17.In which quadrant does the point (7, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
18. 18.What is the distance between the points (2, 5) and (14, 14)? (a) 225 (b) 15 (c) 21 (d) 16
19. 19.In which quadrant does the point (−5, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
20. 20.In which quadrant does the point (3, −9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
21. 21.In which quadrant does the point (−4, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
22. 22.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
23. 23.What is the distance between the points (6, 2) and (11, 14)? (a) 169 (b) 13 (c) 17 (d) 14
24. 24.What is the distance between the points (7, 2) and (22, 10)? (a) 23 (b) 18 (c) 17 (d) 289
25. 25.What is the distance between the points (4, 7) and (16, 23)? (a) 20 (b) 28 (c) 21 (d) 400
26. 26.What is the distance between the points (5, 5) and (10, 17)? (a) 17 (b) 169 (c) 14 (d) 13
27. 27.What is the midpoint of the line joining (0, 17) and (2, 7)? (a) (1, 5) (b) (1, 12) (c) (12, 1) (d) (2, 24)
28. 28.In which quadrant does the point (−2, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
29. 29.What is the distance between the points (0, 7) and (3, 11)? (a) 7 (b) 25 (c) 5 (d) 6
30. 30.What is the distance between the points (2, 8) and (11, 20)? (a) 21 (b) 225 (c) 16 (d) 15
31. 31.What is the midpoint of the line joining (7, 6) and (11, 14)? (a) (9, 10) (b) (2, 4) (c) (10, 9) (d) (18, 20)
32. 32.What is the distance between the points (2, 3) and (7, 15)? (a) 14 (b) 13 (c) 17 (d) 169
33. 33.What is the midpoint of the line joining (5, 9) and (13, 15)? (a) (18, 24) (b) (12, 9) (c) (4, 3) (d) (9, 12)
34. 34.What is the midpoint of the line joining (0, 5) and (12, 11)? (a) (6, 3) (b) (6, 8) (c) (12, 16) (d) (8, 6)
35. 35.What is the midpoint of the line joining (0, 2) and (2, 4)? (a) (3, 1) (b) (1, 3) (c) (1, 1) (d) (2, 6)
36. 36.In which quadrant does the point (−8, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
37. 37.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
38. 38.What is the distance between the points (1, 6) and (5, 3)? (a) 25 (b) 7 (c) 5 (d) 6
39. 39.What is the midpoint of the line joining (7, 9) and (9, 15)? (a) (16, 24) (b) (12, 8) (c) (1, 3) (d) (8, 12)
40. 40.In which quadrant does the point (1, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant

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