Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 222 · 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 (1, 18) and (6, 6)? (a) 13 (b) 17 (c) 169 (d) 14
2. 2.What is the distance between the points (7, 9) and (14, 33)? (a) 31 (b) 625 (c) 26 (d) 25
3. 3.In which quadrant does the point (−2, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
4. 4.What is the distance between the points (1, 21) and (13, 5)? (a) 21 (b) 400 (c) 20 (d) 28
5. 5.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
6. 6.What is the distance between the points (9, 20) and (17, 5)? (a) 17 (b) 289 (c) 23 (d) 18
7. 7.What is the distance between the points (1, 1) and (4, 5)? (a) 25 (b) 6 (c) 5 (d) 7
8. 8.In which quadrant does the point (4, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
9. 9.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
10. 10.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
11. 11.What is the midpoint of the line joining (7, 9) and (9, 19)? (a) (8, 14) (b) (16, 28) (c) (14, 8) (d) (1, 5)
12. 12.In which quadrant does the point (5, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
13. 13.What is the midpoint of the line joining (3, 1) and (11, 7)? (a) (4, 7) (b) (14, 8) (c) (7, 4) (d) (4, 3)
14. 14.What is the distance between the points (0, 4) and (24, 11)? (a) 26 (b) 25 (c) 31 (d) 625
15. 15.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
16. 16.What is the midpoint of the line joining (2, 2) and (10, 4)? (a) (4, 1) (b) (6, 3) (c) (12, 6) (d) (3, 6)
17. 17.In which quadrant does the point (−3, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
18. 18.What is the midpoint of the line joining (2, 4) and (8, 6)? (a) (3, 1) (b) (10, 10) (c) (5, 5) (d) (6, 5)
19. 19.In which quadrant does the point (−3, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
20. 20.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
21. 21.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
22. 22.What is the midpoint of the line joining (4, 5) and (12, 3)? (a) (4, 8) (b) (4, 1) (c) (8, 4) (d) (16, 8)
23. 23.What is the midpoint of the line joining (5, 19) and (13, 7)? (a) (4, 6) (b) (18, 26) (c) (13, 9) (d) (9, 13)
24. 24.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
25. 25.What is the midpoint of the line joining (2, 14) and (10, 10)? (a) (6, 12) (b) (12, 24) (c) (4, 2) (d) (12, 6)
26. 26.What is the midpoint of the line joining (0, 7) and (12, 3)? (a) (12, 10) (b) (5, 6) (c) (6, 5) (d) (6, 2)
27. 27.What is the midpoint of the line joining (8, 0) and (12, 4)? (a) (2, 2) (b) (10, 2) (c) (20, 4) (d) (2, 10)
28. 28.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
29. 29.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
30. 30.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
31. 31.What is the midpoint of the line joining (4, 16) and (10, 4)? (a) (3, 6) (b) (14, 20) (c) (10, 7) (d) (7, 10)
32. 32.What is the midpoint of the line joining (3, 3) and (13, 9)? (a) (16, 12) (b) (6, 8) (c) (8, 6) (d) (5, 3)
33. 33.What is the distance between the points (5, 0) and (9, 3)? (a) 5 (b) 6 (c) 7 (d) 25
34. 34.What is the distance between the points (0, 7) and (6, 15)? (a) 100 (b) 11 (c) 10 (d) 14
35. 35.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
36. 36.In which quadrant does the point (8, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
37. 37.What is the midpoint of the line joining (4, 14) and (6, 4)? (a) (9, 5) (b) (1, 5) (c) (5, 9) (d) (10, 18)
38. 38.In which quadrant does the point (−1, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
39. 39.What is the midpoint of the line joining (5, 5) and (15, 11)? (a) (20, 16) (b) (8, 10) (c) (10, 8) (d) (5, 3)
40. 40.In which quadrant does the point (6, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant

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