Coordinate Geometry Worksheet for Maths Olympiad

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

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