Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 605 · 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, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
2. 2.In which quadrant does the point (−5, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
3. 3.What is the distance between the points (5, 15) and (10, 3)? (a) 13 (b) 169 (c) 14 (d) 17
4. 4.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
5. 5.What is the distance between the points (3, 9) and (7, 6)? (a) 7 (b) 6 (c) 5 (d) 25
6. 6.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
7. 7.In which quadrant does the point (−3, −4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
8. 8.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
9. 9.What is the distance between the points (4, 5) and (9, 17)? (a) 13 (b) 17 (c) 14 (d) 169
10. 10.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
11. 11.In which quadrant does the point (−7, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
12. 12.What is the distance between the points (1, 11) and (4, 7)? (a) 6 (b) 5 (c) 7 (d) 25
13. 13.What is the midpoint of the line joining (10, 6) and (14, 4)? (a) (24, 10) (b) (12, 5) (c) (5, 12) (d) (2, 1)
14. 14.What is the distance between the points (1, 5) and (4, 1)? (a) 6 (b) 25 (c) 7 (d) 5
15. 15.In which quadrant does the point (3, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
16. 16.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
17. 17.What is the distance between the points (0, 6) and (12, 22)? (a) 28 (b) 20 (c) 21 (d) 400
18. 18.What is the distance between the points (2, 21) and (11, 9)? (a) 21 (b) 16 (c) 15 (d) 225
19. 19.In which quadrant does the point (6, −1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
20. 20.What is the midpoint of the line joining (3, 0) and (7, 4)? (a) (2, 5) (b) (2, 2) (c) (10, 4) (d) (5, 2)
21. 21.What is the distance between the points (8, 0) and (20, 5)? (a) 169 (b) 17 (c) 13 (d) 14
22. 22.What is the midpoint of the line joining (6, 2) and (10, 8)? (a) (2, 3) (b) (5, 8) (c) (8, 5) (d) (16, 10)
23. 23.What is the distance between the points (3, 8) and (15, 3)? (a) 169 (b) 17 (c) 13 (d) 14
24. 24.What is the midpoint of the line joining (1, 5) and (13, 7)? (a) (6, 7) (b) (6, 1) (c) (14, 12) (d) (7, 6)
25. 25.In which quadrant does the point (9, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
26. 26.In which quadrant does the point (3, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
27. 27.What is the midpoint of the line joining (5, 6) and (15, 0)? (a) (3, 10) (b) (10, 3) (c) (5, 3) (d) (20, 6)
28. 28.What is the midpoint of the line joining (3, 2) and (15, 0)? (a) (1, 9) (b) (18, 2) (c) (6, 1) (d) (9, 1)
29. 29.What is the distance between the points (4, 8) and (9, 20)? (a) 17 (b) 14 (c) 169 (d) 13
30. 30.What is the distance between the points (0, 15) and (15, 7)? (a) 23 (b) 17 (c) 289 (d) 18
31. 31.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
32. 32.What is the distance between the points (7, 2) and (19, 7)? (a) 17 (b) 169 (c) 13 (d) 14
33. 33.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
34. 34.What is the midpoint of the line joining (5, 1) and (7, 5)? (a) (1, 2) (b) (12, 6) (c) (6, 3) (d) (3, 6)
35. 35.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
36. 36.In which quadrant does the point (8, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
37. 37.What is the distance between the points (1, 20) and (6, 8)? (a) 17 (b) 169 (c) 13 (d) 14
38. 38.In which quadrant does the point (−1, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
39. 39.What is the distance between the points (1, 15) and (25, 8)? (a) 31 (b) 26 (c) 25 (d) 625
40. 40.What is the distance between the points (8, 10) and (12, 7)? (a) 5 (b) 6 (c) 7 (d) 25

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