Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 316 · 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 (3, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
2. 2.In which quadrant does the point (−1, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
3. 3.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
4. 4.What is the distance between the points (3, 9) and (18, 17)? (a) 18 (b) 289 (c) 23 (d) 17
5. 5.In which quadrant does the point (4, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
6. 6.What is the midpoint of the line joining (6, 17) and (16, 7)? (a) (5, 5) (b) (11, 12) (c) (22, 24) (d) (12, 11)
7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
8. 8.In which quadrant does the point (−2, −7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
9. 9.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
10. 10.What is the distance between the points (2, 2) and (14, 7)? (a) 17 (b) 169 (c) 13 (d) 14
11. 11.What is the distance between the points (1, 15) and (6, 3)? (a) 17 (b) 169 (c) 14 (d) 13
12. 12.In which quadrant does the point (−3, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
13. 13.What is the distance between the points (6, 19) and (14, 4)? (a) 23 (b) 289 (c) 17 (d) 18
14. 14.What is the distance between the points (5, 12) and (13, 6)? (a) 11 (b) 10 (c) 100 (d) 14
15. 15.What is the distance between the points (3, 13) and (15, 8)? (a) 13 (b) 169 (c) 14 (d) 17
16. 16.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
17. 17.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
18. 18.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
19. 19.What is the midpoint of the line joining (7, 16) and (9, 10)? (a) (13, 8) (b) (1, 3) (c) (16, 26) (d) (8, 13)
20. 20.What is the midpoint of the line joining (8, 10) and (20, 8)? (a) (9, 14) (b) (6, 1) (c) (28, 18) (d) (14, 9)
21. 21.In which quadrant does the point (4, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
22. 22.What is the midpoint of the line joining (10, 4) and (12, 6)? (a) (22, 10) (b) (1, 1) (c) (5, 11) (d) (11, 5)
23. 23.What is the midpoint of the line joining (0, 21) and (8, 9)? (a) (4, 15) (b) (4, 6) (c) (8, 30) (d) (15, 4)
24. 24.What is the distance between the points (2, 1) and (14, 17)? (a) 21 (b) 20 (c) 400 (d) 28
25. 25.In which quadrant does the point (1, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
26. 26.In which quadrant does the point (6, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
27. 27.What is the midpoint of the line joining (1, 2) and (9, 10)? (a) (10, 12) (b) (6, 5) (c) (5, 6) (d) (4, 4)
28. 28.In which quadrant does the point (−6, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
29. 29.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
30. 30.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
31. 31.In which quadrant does the point (5, −9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
32. 32.In which quadrant does the point (7, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
33. 33.In which quadrant does the point (2, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
34. 34.What is the distance between the points (8, 5) and (15, 29)? (a) 625 (b) 31 (c) 26 (d) 25
35. 35.What is the distance between the points (4, 0) and (12, 15)? (a) 18 (b) 23 (c) 289 (d) 17
36. 36.In which quadrant does the point (8, −6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
37. 37.What is the midpoint of the line joining (2, 0) and (14, 4)? (a) (2, 8) (b) (16, 4) (c) (8, 2) (d) (6, 2)
38. 38.What is the midpoint of the line joining (2, 1) and (4, 5)? (a) (4, 3) (b) (6, 6) (c) (1, 2) (d) (3, 3)
39. 39.In which quadrant does the point (8, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
40. 40.In which quadrant does the point (1, 7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant

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