Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 586 · 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 (5, 13) and (29, 6)? (a) 31 (b) 26 (c) 625 (d) 25
2. 2.What is the midpoint of the line joining (0, 9) and (2, 13)? (a) (11, 1) (b) (2, 22) (c) (1, 11) (d) (1, 2)
3. 3.What is the midpoint of the line joining (10, 10) and (18, 4)? (a) (7, 14) (b) (4, 3) (c) (28, 14) (d) (14, 7)
4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
5. 5.In which quadrant does the point (−1, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
6. 6.What is the midpoint of the line joining (9, 8) and (13, 14)? (a) (22, 22) (b) (11, 11) (c) (12, 11) (d) (2, 3)
7. 7.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
8. 8.In which quadrant does the point (3, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
9. 9.What is the distance between the points (3, 7) and (12, 19)? (a) 225 (b) 21 (c) 15 (d) 16
10. 10.What is the distance between the points (5, 17) and (11, 9)? (a) 100 (b) 11 (c) 10 (d) 14
11. 11.What is the distance between the points (4, 0) and (12, 6)? (a) 10 (b) 11 (c) 100 (d) 14
12. 12.In which quadrant does the point (6, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
13. 13.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
14. 14.In which quadrant does the point (−2, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
15. 15.What is the distance between the points (8, 15) and (17, 3)? (a) 225 (b) 21 (c) 16 (d) 15
16. 16.In which quadrant does the point (−3, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
17. 17.What is the distance between the points (8, 7) and (20, 23)? (a) 20 (b) 400 (c) 28 (d) 21
18. 18.What is the midpoint of the line joining (3, 22) and (13, 10)? (a) (8, 16) (b) (5, 6) (c) (16, 8) (d) (16, 32)
19. 19.What is the midpoint of the line joining (9, 5) and (19, 3)? (a) (4, 14) (b) (14, 4) (c) (28, 8) (d) (5, 1)
20. 20.In which quadrant does the point (−5, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
21. 21.What is the distance between the points (1, 4) and (13, 13)? (a) 225 (b) 21 (c) 16 (d) 15
22. 22.In which quadrant does the point (3, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
23. 23.In which quadrant does the point (1, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
24. 24.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
25. 25.In which quadrant does the point (−3, 4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
26. 26.What is the midpoint of the line joining (6, 18) and (14, 10)? (a) (10, 14) (b) (4, 4) (c) (20, 28) (d) (14, 10)
27. 27.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
28. 28.What is the midpoint of the line joining (5, 2) and (7, 0)? (a) (1, 6) (b) (1, 1) (c) (12, 2) (d) (6, 1)
29. 29.What is the distance between the points (8, 3) and (20, 19)? (a) 28 (b) 20 (c) 400 (d) 21
30. 30.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
31. 31.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
32. 32.In which quadrant does the point (−9, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
33. 33.What is the distance between the points (2, 5) and (14, 0)? (a) 13 (b) 14 (c) 169 (d) 17
34. 34.What is the distance between the points (2, 6) and (7, 18)? (a) 17 (b) 13 (c) 14 (d) 169
35. 35.In which quadrant does the point (3, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
36. 36.What is the distance between the points (2, 9) and (17, 1)? (a) 17 (b) 18 (c) 23 (d) 289
37. 37.What is the distance between the points (1, 14) and (10, 2)? (a) 16 (b) 15 (c) 225 (d) 21
38. 38.In which quadrant does the point (−6, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
39. 39.What is the distance between the points (0, 1) and (8, 16)? (a) 17 (b) 289 (c) 18 (d) 23
40. 40.What is the distance between the points (2, 21) and (18, 9)? (a) 400 (b) 21 (c) 28 (d) 20

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