Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 684 · 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 (9, 20) and (17, 5)? (a) 18 (b) 23 (c) 17 (d) 289
2. 2.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
3. 3.What is the distance between the points (5, 0) and (13, 15)? (a) 289 (b) 23 (c) 18 (d) 17
4. 4.In which quadrant does the point (−1, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
5. 5.What is the midpoint of the line joining (3, 9) and (15, 11)? (a) (9, 10) (b) (10, 9) (c) (6, 1) (d) (18, 20)
6. 6.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
7. 7.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
8. 8.In which quadrant does the point (−9, −9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
9. 9.What is the midpoint of the line joining (8, 10) and (16, 14)? (a) (4, 2) (b) (13, 12) (c) (12, 12) (d) (24, 24)
10. 10.What is the distance between the points (6, 15) and (11, 3)? (a) 17 (b) 14 (c) 13 (d) 169
11. 11.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
12. 12.In which quadrant does the point (4, 6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
13. 13.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
14. 14.In which quadrant does the point (8, −7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
15. 15.In which quadrant does the point (9, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
16. 16.What is the midpoint of the line joining (5, 16) and (17, 6)? (a) (22, 22) (b) (12, 11) (c) (6, 5) (d) (11, 11)
17. 17.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
18. 18.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
19. 19.In which quadrant does the point (9, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
20. 20.What is the distance between the points (5, 9) and (11, 1)? (a) 14 (b) 100 (c) 10 (d) 11
21. 21.What is the distance between the points (2, 2) and (5, 6)? (a) 6 (b) 25 (c) 7 (d) 5
22. 22.What is the midpoint of the line joining (1, 4) and (13, 0)? (a) (6, 2) (b) (2, 7) (c) (14, 4) (d) (7, 2)
23. 23.In which quadrant does the point (−6, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
24. 24.What is the distance between the points (2, 17) and (11, 5)? (a) 16 (b) 225 (c) 21 (d) 15
25. 25.What is the midpoint of the line joining (8, 9) and (12, 17)? (a) (2, 4) (b) (10, 13) (c) (20, 26) (d) (13, 10)
26. 26.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
27. 27.What is the distance between the points (9, 3) and (13, 6)? (a) 25 (b) 7 (c) 6 (d) 5
28. 28.What is the distance between the points (0, 0) and (12, 5)? (a) 17 (b) 14 (c) 169 (d) 13
29. 29.What is the distance between the points (3, 0) and (7, 3)? (a) 6 (b) 25 (c) 5 (d) 7
30. 30.What is the midpoint of the line joining (9, 8) and (15, 20)? (a) (24, 28) (b) (12, 14) (c) (3, 6) (d) (14, 12)
31. 31.In which quadrant does the point (−1, 5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
32. 32.What is the distance between the points (2, 4) and (9, 28)? (a) 26 (b) 25 (c) 31 (d) 625
33. 33.In which quadrant does the point (8, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
34. 34.What is the midpoint of the line joining (1, 15) and (11, 3)? (a) (6, 9) (b) (9, 6) (c) (12, 18) (d) (5, 6)
35. 35.What is the distance between the points (9, 5) and (21, 0)? (a) 14 (b) 169 (c) 17 (d) 13
36. 36.In which quadrant does the point (5, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
37. 37.What is the distance between the points (5, 2) and (29, 9)? (a) 31 (b) 625 (c) 26 (d) 25
38. 38.What is the distance between the points (9, 7) and (17, 1)? (a) 11 (b) 100 (c) 10 (d) 14
39. 39.What is the midpoint of the line joining (10, 8) and (12, 18)? (a) (13, 11) (b) (11, 13) (c) (22, 26) (d) (1, 5)
40. 40.What is the midpoint of the line joining (3, 4) and (9, 2)? (a) (3, 6) (b) (12, 6) (c) (3, 1) (d) (6, 3)

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