Coordinate Geometry Worksheet for Maths Olympiad

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

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