Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 889 · 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 (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
2. 2.What is the midpoint of the line joining (4, 6) and (6, 14)? (a) (10, 20) (b) (1, 4) (c) (10, 5) (d) (5, 10)
3. 3.What is the midpoint of the line joining (0, 5) and (10, 9)? (a) (5, 7) (b) (5, 2) (c) (7, 5) (d) (10, 14)
4. 4.What is the midpoint of the line joining (2, 7) and (14, 17)? (a) (12, 8) (b) (16, 24) (c) (6, 5) (d) (8, 12)
5. 5.In which quadrant does the point (4, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
6. 6.What is the midpoint of the line joining (5, 5) and (11, 9)? (a) (7, 8) (b) (16, 14) (c) (3, 2) (d) (8, 7)
7. 7.What is the distance between the points (8, 17) and (17, 5)? (a) 16 (b) 21 (c) 225 (d) 15
8. 8.What is the midpoint of the line joining (5, 8) and (13, 2)? (a) (5, 9) (b) (4, 3) (c) (18, 10) (d) (9, 5)
9. 9.What is the midpoint of the line joining (2, 12) and (8, 10)? (a) (10, 22) (b) (11, 5) (c) (3, 1) (d) (5, 11)
10. 10.What is the distance between the points (5, 14) and (17, 9)? (a) 169 (b) 14 (c) 17 (d) 13
11. 11.What is the distance between the points (4, 0) and (11, 24)? (a) 31 (b) 625 (c) 26 (d) 25
12. 12.What is the distance between the points (5, 1) and (10, 13)? (a) 14 (b) 13 (c) 169 (d) 17
13. 13.What is the distance between the points (3, 8) and (8, 20)? (a) 14 (b) 13 (c) 169 (d) 17
14. 14.What is the distance between the points (1, 8) and (7, 0)? (a) 10 (b) 100 (c) 11 (d) 14
15. 15.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
16. 16.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
17. 17.In which quadrant does the point (9, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
18. 18.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
19. 19.What is the distance between the points (9, 7) and (13, 4)? (a) 5 (b) 6 (c) 25 (d) 7
20. 20.In which quadrant does the point (−8, −9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
21. 21.What is the distance between the points (4, 17) and (13, 5)? (a) 16 (b) 225 (c) 21 (d) 15
22. 22.In which quadrant does the point (6, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
23. 23.In which quadrant does the point (7, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
24. 24.What is the midpoint of the line joining (7, 15) and (15, 7)? (a) (11, 11) (b) (4, 4) (c) (12, 11) (d) (22, 22)
25. 25.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
26. 26.In which quadrant does the point (7, −4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
27. 27.In which quadrant does the point (9, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
28. 28.What is the distance between the points (9, 14) and (25, 2)? (a) 400 (b) 28 (c) 20 (d) 21
29. 29.In which quadrant does the point (5, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
30. 30.What is the distance between the points (4, 8) and (9, 20)? (a) 169 (b) 14 (c) 17 (d) 13
31. 31.What is the distance between the points (5, 8) and (10, 20)? (a) 13 (b) 17 (c) 14 (d) 169
32. 32.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
33. 33.What is the distance between the points (9, 1) and (12, 5)? (a) 5 (b) 6 (c) 25 (d) 7
34. 34.In which quadrant does the point (−2, −4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
35. 35.What is the midpoint of the line joining (3, 0) and (7, 8)? (a) (2, 4) (b) (4, 5) (c) (5, 4) (d) (10, 8)
36. 36.In which quadrant does the point (1, −7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
37. 37.In which quadrant does the point (−1, 1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
38. 38.What is the midpoint of the line joining (8, 7) and (12, 17)? (a) (2, 5) (b) (20, 24) (c) (10, 12) (d) (12, 10)
39. 39.What is the midpoint of the line joining (1, 8) and (3, 6)? (a) (7, 2) (b) (2, 7) (c) (1, 1) (d) (4, 14)
40. 40.What is the midpoint of the line joining (6, 9) and (18, 15)? (a) (12, 12) (b) (6, 3) (c) (24, 24) (d) (13, 12)

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