Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 328 · 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, 17) and (5, 5)? (a) 17 (b) 169 (c) 14 (d) 13
2. 2.In which quadrant does the point (1, 6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
3. 3.What is the distance between the points (0, 4) and (24, 11)? (a) 26 (b) 31 (c) 25 (d) 625
4. 4.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
5. 5.What is the midpoint of the line joining (10, 4) and (16, 12)? (a) (8, 13) (b) (13, 8) (c) (26, 16) (d) (3, 4)
6. 6.What is the midpoint of the line joining (6, 20) and (12, 10)? (a) (18, 30) (b) (3, 5) (c) (9, 15) (d) (15, 9)
7. 7.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
8. 8.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
9. 9.In which quadrant does the point (1, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
10. 10.In which quadrant does the point (−5, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
11. 11.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
12. 12.In which quadrant does the point (2, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
13. 13.What is the midpoint of the line joining (10, 8) and (18, 2)? (a) (4, 3) (b) (14, 5) (c) (5, 14) (d) (28, 10)
14. 14.What is the midpoint of the line joining (9, 16) and (19, 6)? (a) (14, 11) (b) (28, 22) (c) (5, 5) (d) (11, 14)
15. 15.What is the distance between the points (0, 0) and (24, 7)? (a) 625 (b) 25 (c) 26 (d) 31
16. 16.What is the distance between the points (3, 18) and (12, 6)? (a) 225 (b) 21 (c) 15 (d) 16
17. 17.What is the midpoint of the line joining (1, 6) and (3, 2)? (a) (4, 8) (b) (2, 4) (c) (1, 2) (d) (4, 2)
18. 18.What is the distance between the points (6, 1) and (18, 6)? (a) 17 (b) 169 (c) 14 (d) 13
19. 19.In which quadrant does the point (8, 2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
20. 20.In which quadrant does the point (−8, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
21. 21.What is the midpoint of the line joining (8, 1) and (18, 13)? (a) (7, 13) (b) (5, 6) (c) (13, 7) (d) (26, 14)
22. 22.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
23. 23.What is the midpoint of the line joining (7, 1) and (9, 11)? (a) (6, 8) (b) (1, 5) (c) (8, 6) (d) (16, 12)
24. 24.What is the distance between the points (5, 9) and (11, 17)? (a) 100 (b) 14 (c) 10 (d) 11
25. 25.What is the distance between the points (0, 1) and (12, 6)? (a) 17 (b) 169 (c) 13 (d) 14
26. 26.What is the distance between the points (2, 0) and (8, 8)? (a) 10 (b) 14 (c) 100 (d) 11
27. 27.In which quadrant does the point (8, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
28. 28.In which quadrant does the point (−2, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
29. 29.What is the distance between the points (3, 8) and (11, 14)? (a) 10 (b) 100 (c) 11 (d) 14
30. 30.What is the midpoint of the line joining (5, 8) and (15, 10)? (a) (9, 10) (b) (10, 9) (c) (5, 1) (d) (20, 18)
31. 31.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
32. 32.What is the distance between the points (6, 9) and (18, 0)? (a) 15 (b) 21 (c) 225 (d) 16
33. 33.What is the midpoint of the line joining (0, 6) and (10, 8)? (a) (10, 14) (b) (5, 7) (c) (5, 1) (d) (7, 5)
34. 34.In which quadrant does the point (6, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
35. 35.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 14 (d) 17
36. 36.What is the distance between the points (5, 8) and (11, 16)? (a) 14 (b) 100 (c) 10 (d) 11
37. 37.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
38. 38.What is the distance between the points (5, 3) and (17, 19)? (a) 21 (b) 28 (c) 400 (d) 20
39. 39.In which quadrant does the point (4, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
40. 40.In which quadrant does the point (9, −8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant

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