Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 553 · 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.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
2. 2.What is the midpoint of the line joining (9, 13) and (11, 7)? (a) (20, 20) (b) (10, 10) (c) (1, 3) (d) (11, 10)
3. 3.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
4. 4.In which quadrant does the point (8, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
5. 5.What is the midpoint of the line joining (1, 1) and (11, 5)? (a) (12, 6) (b) (5, 2) (c) (3, 6) (d) (6, 3)
6. 6.In which quadrant does the point (−3, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
7. 7.In which quadrant does the point (−4, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
8. 8.What is the distance between the points (4, 23) and (12, 8)? (a) 17 (b) 289 (c) 18 (d) 23
9. 9.What is the midpoint of the line joining (9, 0) and (21, 4)? (a) (30, 4) (b) (6, 2) (c) (2, 15) (d) (15, 2)
10. 10.What is the distance between the points (7, 17) and (12, 5)? (a) 169 (b) 13 (c) 14 (d) 17
11. 11.In which quadrant does the point (−1, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
12. 12.In which quadrant does the point (−8, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
13. 13.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
14. 14.What is the distance between the points (7, 2) and (23, 14)? (a) 20 (b) 28 (c) 21 (d) 400
15. 15.What is the distance between the points (0, 4) and (4, 7)? (a) 25 (b) 5 (c) 7 (d) 6
16. 16.What is the distance between the points (5, 10) and (11, 2)? (a) 100 (b) 14 (c) 10 (d) 11
17. 17.In which quadrant does the point (−2, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
18. 18.In which quadrant does the point (2, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
19. 19.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
20. 20.What is the midpoint of the line joining (10, 14) and (20, 2)? (a) (8, 15) (b) (5, 6) (c) (15, 8) (d) (30, 16)
21. 21.What is the midpoint of the line joining (4, 12) and (16, 0)? (a) (20, 12) (b) (10, 6) (c) (6, 10) (d) (6, 6)
22. 22.In which quadrant does the point (−9, −4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
23. 23.In which quadrant does the point (−1, −6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
24. 24.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
25. 25.In which quadrant does the point (5, −8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
26. 26.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
27. 27.What is the distance between the points (0, 7) and (12, 2)? (a) 17 (b) 13 (c) 14 (d) 169
28. 28.What is the midpoint of the line joining (0, 9) and (2, 15)? (a) (2, 24) (b) (12, 1) (c) (1, 3) (d) (1, 12)
29. 29.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
30. 30.What is the midpoint of the line joining (8, 9) and (20, 17)? (a) (28, 26) (b) (13, 14) (c) (6, 4) (d) (14, 13)
31. 31.What is the distance between the points (1, 13) and (6, 1)? (a) 14 (b) 17 (c) 13 (d) 169
32. 32.In which quadrant does the point (6, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
33. 33.What is the midpoint of the line joining (3, 15) and (9, 7)? (a) (12, 22) (b) (3, 4) (c) (6, 11) (d) (11, 6)
34. 34.What is the distance between the points (2, 0) and (18, 12)? (a) 21 (b) 28 (c) 400 (d) 20
35. 35.What is the distance between the points (1, 1) and (13, 10)? (a) 16 (b) 15 (c) 225 (d) 21
36. 36.In which quadrant does the point (−8, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
37. 37.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
38. 38.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
39. 39.In which quadrant does the point (−7, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
40. 40.What is the distance between the points (2, 8) and (10, 14)? (a) 14 (b) 100 (c) 11 (d) 10

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