Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 476 · 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 midpoint of the line joining (8, 19) and (10, 7)? (a) (18, 26) (b) (9, 13) (c) (1, 6) (d) (13, 9)
2. 2.What is the distance between the points (8, 6) and (15, 30)? (a) 25 (b) 26 (c) 625 (d) 31
3. 3.In which quadrant does the point (5, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
4. 4.What is the distance between the points (0, 8) and (4, 5)? (a) 7 (b) 25 (c) 5 (d) 6
5. 5.What is the distance between the points (7, 8) and (13, 0)? (a) 100 (b) 14 (c) 10 (d) 11
6. 6.What is the distance between the points (8, 5) and (16, 20)? (a) 23 (b) 17 (c) 18 (d) 289
7. 7.In which quadrant does the point (5, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
8. 8.What is the midpoint of the line joining (6, 15) and (18, 9)? (a) (6, 3) (b) (24, 24) (c) (13, 12) (d) (12, 12)
9. 9.What is the distance between the points (7, 14) and (19, 9)? (a) 169 (b) 14 (c) 13 (d) 17
10. 10.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
11. 11.What is the distance between the points (6, 3) and (13, 27)? (a) 26 (b) 25 (c) 31 (d) 625
12. 12.What is the midpoint of the line joining (9, 16) and (13, 6)? (a) (12, 11) (b) (11, 11) (c) (22, 22) (d) (2, 5)
13. 13.In which quadrant does the point (−1, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
14. 14.What is the distance between the points (7, 20) and (19, 4)? (a) 400 (b) 21 (c) 28 (d) 20
15. 15.In which quadrant does the point (−1, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
16. 16.In which quadrant does the point (−8, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
17. 17.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
18. 18.What is the distance between the points (5, 5) and (17, 14)? (a) 16 (b) 225 (c) 21 (d) 15
19. 19.In which quadrant does the point (−2, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
20. 20.In which quadrant does the point (−2, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
21. 21.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
22. 22.What is the distance between the points (6, 1) and (18, 17)? (a) 21 (b) 400 (c) 28 (d) 20
23. 23.In which quadrant does the point (−9, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
24. 24.What is the midpoint of the line joining (5, 5) and (7, 9)? (a) (7, 6) (b) (12, 14) (c) (1, 2) (d) (6, 7)
25. 25.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
26. 26.In which quadrant does the point (−1, −8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
27. 27.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
28. 28.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
29. 29.What is the distance between the points (0, 3) and (8, 9)? (a) 10 (b) 14 (c) 11 (d) 100
30. 30.In which quadrant does the point (2, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
31. 31.What is the midpoint of the line joining (7, 13) and (11, 5)? (a) (2, 4) (b) (9, 9) (c) (18, 18) (d) (10, 9)
32. 32.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
33. 33.What is the midpoint of the line joining (0, 5) and (4, 1)? (a) (2, 2) (b) (3, 2) (c) (4, 6) (d) (2, 3)
34. 34.In which quadrant does the point (9, −1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
35. 35.What is the midpoint of the line joining (0, 18) and (8, 10)? (a) (8, 28) (b) (14, 4) (c) (4, 14) (d) (4, 4)
36. 36.What is the midpoint of the line joining (2, 11) and (12, 5)? (a) (5, 3) (b) (7, 8) (c) (14, 16) (d) (8, 7)
37. 37.What is the distance between the points (4, 1) and (16, 6)? (a) 14 (b) 17 (c) 13 (d) 169
38. 38.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
39. 39.What is the distance between the points (7, 9) and (11, 6)? (a) 5 (b) 25 (c) 7 (d) 6
40. 40.In which quadrant does the point (−2, 7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant

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