Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 994 · 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 (4, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
2. 2.What is the distance between the points (7, 2) and (13, 10)? (a) 11 (b) 10 (c) 100 (d) 14
3. 3.What is the midpoint of the line joining (4, 7) and (6, 9)? (a) (10, 16) (b) (8, 5) (c) (1, 1) (d) (5, 8)
4. 4.What is the midpoint of the line joining (2, 8) and (12, 18)? (a) (14, 26) (b) (5, 5) (c) (7, 13) (d) (13, 7)
5. 5.In which quadrant does the point (9, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
6. 6.What is the distance between the points (7, 20) and (19, 4)? (a) 400 (b) 21 (c) 28 (d) 20
7. 7.What is the distance between the points (9, 16) and (14, 4)? (a) 17 (b) 13 (c) 169 (d) 14
8. 8.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
9. 9.In which quadrant does the point (−3, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
10. 10.What is the distance between the points (4, 15) and (20, 3)? (a) 20 (b) 400 (c) 21 (d) 28
11. 11.What is the distance between the points (0, 9) and (12, 4)? (a) 14 (b) 13 (c) 169 (d) 17
12. 12.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
13. 13.What is the midpoint of the line joining (4, 7) and (10, 11)? (a) (3, 2) (b) (9, 7) (c) (14, 18) (d) (7, 9)
14. 14.What is the distance between the points (3, 6) and (15, 15)? (a) 15 (b) 225 (c) 21 (d) 16
15. 15.What is the distance between the points (8, 20) and (24, 8)? (a) 400 (b) 20 (c) 21 (d) 28
16. 16.What is the distance between the points (6, 12) and (11, 0)? (a) 13 (b) 169 (c) 17 (d) 14
17. 17.What is the midpoint of the line joining (3, 6) and (13, 18)? (a) (8, 12) (b) (5, 6) (c) (12, 8) (d) (16, 24)
18. 18.What is the midpoint of the line joining (2, 9) and (12, 1)? (a) (5, 4) (b) (14, 10) (c) (7, 5) (d) (5, 7)
19. 19.What is the distance between the points (1, 12) and (9, 6)? (a) 100 (b) 10 (c) 11 (d) 14
20. 20.What is the distance between the points (9, 3) and (13, 0)? (a) 25 (b) 6 (c) 7 (d) 5
21. 21.What is the distance between the points (1, 5) and (4, 1)? (a) 25 (b) 5 (c) 6 (d) 7
22. 22.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 11 (d) 14
23. 23.What is the distance between the points (6, 15) and (18, 6)? (a) 21 (b) 225 (c) 15 (d) 16
24. 24.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
25. 25.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
26. 26.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
27. 27.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
28. 28.In which quadrant does the point (5, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
29. 29.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
30. 30.What is the distance between the points (8, 13) and (11, 9)? (a) 7 (b) 25 (c) 5 (d) 6
31. 31.What is the distance between the points (5, 4) and (13, 10)? (a) 14 (b) 11 (c) 10 (d) 100
32. 32.What is the midpoint of the line joining (9, 17) and (11, 5)? (a) (10, 11) (b) (1, 6) (c) (11, 10) (d) (20, 22)
33. 33.What is the distance between the points (1, 4) and (7, 12)? (a) 10 (b) 100 (c) 11 (d) 14
34. 34.What is the midpoint of the line joining (5, 18) and (9, 6)? (a) (12, 7) (b) (2, 6) (c) (7, 12) (d) (14, 24)
35. 35.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
36. 36.In which quadrant does the point (4, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
37. 37.In which quadrant does the point (−8, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
38. 38.What is the distance between the points (1, 1) and (13, 10)? (a) 21 (b) 225 (c) 16 (d) 15
39. 39.In which quadrant does the point (1, −5) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
40. 40.What is the midpoint of the line joining (7, 16) and (15, 6)? (a) (4, 5) (b) (11, 11) (c) (22, 22) (d) (12, 11)

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