Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 227 · 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, 1) and (7, 13)? (a) 13 (b) 169 (c) 17 (d) 14
2. 2.What is the midpoint of the line joining (4, 16) and (8, 8)? (a) (12, 6) (b) (2, 4) (c) (6, 12) (d) (12, 24)
3. 3.What is the midpoint of the line joining (0, 6) and (12, 16)? (a) (11, 6) (b) (6, 11) (c) (6, 5) (d) (12, 22)
4. 4.In which quadrant does the point (3, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
5. 5.What is the distance between the points (6, 24) and (13, 0)? (a) 625 (b) 31 (c) 25 (d) 26
6. 6.What is the midpoint of the line joining (9, 15) and (15, 9)? (a) (3, 3) (b) (24, 24) (c) (12, 12) (d) (13, 12)
7. 7.What is the distance between the points (7, 18) and (19, 2)? (a) 28 (b) 400 (c) 21 (d) 20
8. 8.In which quadrant does the point (1, −2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
9. 9.What is the midpoint of the line joining (3, 20) and (15, 10)? (a) (15, 9) (b) (6, 5) (c) (18, 30) (d) (9, 15)
10. 10.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
11. 11.What is the midpoint of the line joining (0, 6) and (4, 14)? (a) (2, 4) (b) (10, 2) (c) (4, 20) (d) (2, 10)
12. 12.What is the distance between the points (1, 15) and (9, 0)? (a) 289 (b) 18 (c) 23 (d) 17
13. 13.What is the distance between the points (8, 17) and (20, 1)? (a) 20 (b) 400 (c) 21 (d) 28
14. 14.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
15. 15.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
16. 16.In which quadrant does the point (−8, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
17. 17.What is the midpoint of the line joining (5, 2) and (7, 4)? (a) (3, 6) (b) (1, 1) (c) (6, 3) (d) (12, 6)
18. 18.What is the midpoint of the line joining (3, 7) and (11, 15)? (a) (14, 22) (b) (4, 4) (c) (11, 7) (d) (7, 11)
19. 19.What is the distance between the points (6, 1) and (11, 13)? (a) 13 (b) 169 (c) 14 (d) 17
20. 20.In which quadrant does the point (5, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
21. 21.What is the distance between the points (2, 8) and (8, 0)? (a) 14 (b) 100 (c) 11 (d) 10
22. 22.What is the distance between the points (3, 1) and (8, 13)? (a) 169 (b) 17 (c) 14 (d) 13
23. 23.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
24. 24.In which quadrant does the point (−4, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
25. 25.In which quadrant does the point (−1, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
26. 26.What is the distance between the points (0, 0) and (5, 12)? (a) 14 (b) 169 (c) 17 (d) 13
27. 27.In which quadrant does the point (9, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
28. 28.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
29. 29.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
30. 30.What is the midpoint of the line joining (9, 3) and (11, 5)? (a) (4, 10) (b) (20, 8) (c) (10, 4) (d) (1, 1)
31. 31.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 21 (d) 225
32. 32.What is the distance between the points (0, 15) and (15, 7)? (a) 17 (b) 289 (c) 23 (d) 18
33. 33.In which quadrant does the point (−7, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
34. 34.In which quadrant does the point (6, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
35. 35.In which quadrant does the point (−4, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
36. 36.What is the midpoint of the line joining (8, 13) and (18, 5)? (a) (5, 4) (b) (26, 18) (c) (13, 9) (d) (9, 13)
37. 37.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
38. 38.What is the distance between the points (8, 7) and (16, 1)? (a) 10 (b) 14 (c) 11 (d) 100
39. 39.What is the distance between the points (2, 13) and (14, 8)? (a) 17 (b) 169 (c) 14 (d) 13
40. 40.What is the midpoint of the line joining (9, 9) and (11, 15)? (a) (12, 10) (b) (20, 24) (c) (10, 12) (d) (1, 3)

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad