Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 438 · 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, 13) and (33, 6)? (a) 31 (b) 26 (c) 625 (d) 25
2. 2.What is the distance between the points (0, 16) and (6, 8)? (a) 100 (b) 14 (c) 10 (d) 11
3. 3.What is the midpoint of the line joining (9, 2) and (15, 0)? (a) (1, 12) (b) (3, 1) (c) (12, 1) (d) (24, 2)
4. 4.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
5. 5.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
6. 6.What is the midpoint of the line joining (5, 5) and (9, 17)? (a) (2, 6) (b) (11, 7) (c) (7, 11) (d) (14, 22)
7. 7.What is the distance between the points (8, 1) and (11, 5)? (a) 7 (b) 6 (c) 5 (d) 25
8. 8.What is the distance between the points (3, 0) and (7, 3)? (a) 7 (b) 25 (c) 6 (d) 5
9. 9.What is the midpoint of the line joining (6, 6) and (8, 14)? (a) (7, 10) (b) (10, 7) (c) (14, 20) (d) (1, 4)
10. 10.What is the distance between the points (5, 3) and (10, 15)? (a) 17 (b) 14 (c) 13 (d) 169
11. 11.What is the midpoint of the line joining (9, 3) and (11, 13)? (a) (20, 16) (b) (8, 10) (c) (1, 5) (d) (10, 8)
12. 12.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
13. 13.In which quadrant does the point (6, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
14. 14.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
15. 15.In which quadrant does the point (−3, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
16. 16.What is the midpoint of the line joining (10, 8) and (22, 10)? (a) (32, 18) (b) (6, 1) (c) (16, 9) (d) (9, 16)
17. 17.What is the midpoint of the line joining (3, 7) and (7, 3)? (a) (2, 2) (b) (10, 10) (c) (6, 5) (d) (5, 5)
18. 18.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
19. 19.In which quadrant does the point (8, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
20. 20.What is the midpoint of the line joining (6, 6) and (10, 10)? (a) (8, 8) (b) (9, 8) (c) (16, 16) (d) (2, 2)
21. 21.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
22. 22.In which quadrant does the point (−2, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
23. 23.In which quadrant does the point (6, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
24. 24.In which quadrant does the point (−1, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
25. 25.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
26. 26.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
27. 27.What is the midpoint of the line joining (1, 1) and (5, 11)? (a) (3, 6) (b) (2, 5) (c) (6, 12) (d) (6, 3)
28. 28.In which quadrant does the point (7, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
29. 29.What is the midpoint of the line joining (3, 8) and (11, 16)? (a) (14, 24) (b) (12, 7) (c) (4, 4) (d) (7, 12)
30. 30.What is the distance between the points (2, 9) and (10, 3)? (a) 14 (b) 10 (c) 100 (d) 11
31. 31.What is the midpoint of the line joining (7, 6) and (19, 16)? (a) (13, 11) (b) (26, 22) (c) (11, 13) (d) (6, 5)
32. 32.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
33. 33.What is the midpoint of the line joining (1, 8) and (3, 10)? (a) (4, 18) (b) (1, 1) (c) (2, 9) (d) (9, 2)
34. 34.What is the distance between the points (3, 1) and (18, 9)? (a) 23 (b) 18 (c) 289 (d) 17
35. 35.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
36. 36.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
37. 37.What is the distance between the points (0, 30) and (7, 6)? (a) 625 (b) 26 (c) 31 (d) 25
38. 38.In which quadrant does the point (8, 9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
39. 39.What is the distance between the points (1, 6) and (13, 1)? (a) 14 (b) 13 (c) 17 (d) 169
40. 40.What is the midpoint of the line joining (9, 0) and (11, 6)? (a) (1, 3) (b) (10, 3) (c) (3, 10) (d) (20, 6)

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