Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 519 · 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 (2, 5) and (10, 20)? (a) 23 (b) 17 (c) 289 (d) 18
2. 2.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
3. 3.In which quadrant does the point (8, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
4. 4.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
5. 5.What is the distance between the points (1, 16) and (13, 0)? (a) 400 (b) 20 (c) 28 (d) 21
6. 6.In which quadrant does the point (2, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
7. 7.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
8. 8.In which quadrant does the point (7, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
9. 9.What is the midpoint of the line joining (8, 1) and (12, 3)? (a) (2, 1) (b) (2, 10) (c) (10, 2) (d) (20, 4)
10. 10.What is the midpoint of the line joining (5, 4) and (9, 12)? (a) (14, 16) (b) (2, 4) (c) (7, 8) (d) (8, 7)
11. 11.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
12. 12.What is the distance between the points (0, 6) and (4, 9)? (a) 7 (b) 25 (c) 6 (d) 5
13. 13.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
14. 14.What is the distance between the points (1, 15) and (6, 3)? (a) 14 (b) 169 (c) 13 (d) 17
15. 15.What is the midpoint of the line joining (5, 11) and (17, 3)? (a) (7, 11) (b) (22, 14) (c) (11, 7) (d) (6, 4)
16. 16.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
17. 17.What is the distance between the points (1, 3) and (13, 8)? (a) 14 (b) 17 (c) 13 (d) 169
18. 18.What is the distance between the points (1, 8) and (13, 17)? (a) 21 (b) 16 (c) 225 (d) 15
19. 19.In which quadrant does the point (−7, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
20. 20.In which quadrant does the point (−6, 1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
21. 21.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
22. 22.In which quadrant does the point (−1, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
23. 23.In which quadrant does the point (7, 5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
24. 24.What is the distance between the points (0, 7) and (12, 12)? (a) 17 (b) 14 (c) 13 (d) 169
25. 25.What is the distance between the points (5, 19) and (21, 7)? (a) 28 (b) 20 (c) 400 (d) 21
26. 26.In which quadrant does the point (−2, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
27. 27.In which quadrant does the point (6, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
28. 28.What is the midpoint of the line joining (7, 3) and (15, 15)? (a) (11, 9) (b) (9, 11) (c) (4, 6) (d) (22, 18)
29. 29.In which quadrant does the point (4, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
30. 30.In which quadrant does the point (−7, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
31. 31.What is the distance between the points (6, 7) and (14, 13)? (a) 11 (b) 14 (c) 10 (d) 100
32. 32.What is the distance between the points (9, 19) and (14, 7)? (a) 13 (b) 169 (c) 14 (d) 17
33. 33.What is the midpoint of the line joining (4, 4) and (14, 12)? (a) (9, 8) (b) (8, 9) (c) (5, 4) (d) (18, 16)
34. 34.In which quadrant does the point (−3, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
35. 35.What is the midpoint of the line joining (10, 15) and (18, 5)? (a) (4, 5) (b) (28, 20) (c) (10, 14) (d) (14, 10)
36. 36.In which quadrant does the point (−7, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
37. 37.What is the distance between the points (2, 31) and (9, 7)? (a) 31 (b) 25 (c) 26 (d) 625
38. 38.In which quadrant does the point (−2, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
39. 39.In which quadrant does the point (6, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
40. 40.What is the distance between the points (9, 14) and (24, 6)? (a) 17 (b) 289 (c) 23 (d) 18

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