Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 782 · 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 (2, 4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
2. 2.In which quadrant does the point (6, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
3. 3.What is the distance between the points (3, 7) and (19, 19)? (a) 20 (b) 21 (c) 400 (d) 28
4. 4.In which quadrant does the point (−6, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
5. 5.In which quadrant does the point (−6, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
6. 6.In which quadrant does the point (6, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
7. 7.What is the distance between the points (8, 10) and (20, 5)? (a) 17 (b) 14 (c) 13 (d) 169
8. 8.What is the distance between the points (0, 12) and (3, 8)? (a) 7 (b) 5 (c) 6 (d) 25
9. 9.What is the distance between the points (2, 9) and (11, 21)? (a) 16 (b) 21 (c) 225 (d) 15
10. 10.What is the midpoint of the line joining (10, 1) and (20, 7)? (a) (5, 3) (b) (15, 4) (c) (30, 8) (d) (4, 15)
11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
12. 12.What is the distance between the points (8, 4) and (20, 13)? (a) 16 (b) 225 (c) 21 (d) 15
13. 13.What is the midpoint of the line joining (5, 2) and (11, 0)? (a) (3, 1) (b) (16, 2) (c) (1, 8) (d) (8, 1)
14. 14.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
15. 15.What is the distance between the points (9, 2) and (13, 5)? (a) 25 (b) 7 (c) 5 (d) 6
16. 16.What is the midpoint of the line joining (7, 10) and (19, 12)? (a) (6, 1) (b) (13, 11) (c) (26, 22) (d) (11, 13)
17. 17.What is the distance between the points (0, 3) and (24, 10)? (a) 625 (b) 31 (c) 26 (d) 25
18. 18.What is the midpoint of the line joining (0, 18) and (4, 10)? (a) (2, 4) (b) (14, 2) (c) (4, 28) (d) (2, 14)
19. 19.In which quadrant does the point (1, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
20. 20.What is the midpoint of the line joining (4, 13) and (6, 1)? (a) (7, 5) (b) (5, 7) (c) (1, 6) (d) (10, 14)
21. 21.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
22. 22.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
23. 23.What is the midpoint of the line joining (10, 15) and (16, 3)? (a) (26, 18) (b) (3, 6) (c) (9, 13) (d) (13, 9)
24. 24.What is the distance between the points (8, 12) and (14, 4)? (a) 100 (b) 10 (c) 14 (d) 11
25. 25.What is the distance between the points (9, 6) and (13, 9)? (a) 7 (b) 6 (c) 5 (d) 25
26. 26.What is the midpoint of the line joining (0, 2) and (8, 6)? (a) (8, 8) (b) (4, 2) (c) (4, 4) (d) (5, 4)
27. 27.What is the distance between the points (7, 8) and (11, 11)? (a) 25 (b) 7 (c) 6 (d) 5
28. 28.In which quadrant does the point (−4, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
29. 29.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
30. 30.What is the distance between the points (2, 16) and (18, 4)? (a) 400 (b) 20 (c) 21 (d) 28
31. 31.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
32. 32.What is the midpoint of the line joining (4, 1) and (6, 13)? (a) (7, 5) (b) (5, 7) (c) (1, 6) (d) (10, 14)
33. 33.What is the distance between the points (6, 24) and (13, 0)? (a) 31 (b) 26 (c) 625 (d) 25
34. 34.What is the distance between the points (8, 2) and (16, 8)? (a) 14 (b) 11 (c) 10 (d) 100
35. 35.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
36. 36.What is the midpoint of the line joining (5, 5) and (17, 1)? (a) (11, 3) (b) (22, 6) (c) (6, 2) (d) (3, 11)
37. 37.What is the distance between the points (9, 9) and (21, 18)? (a) 15 (b) 225 (c) 21 (d) 16
38. 38.What is the midpoint of the line joining (2, 16) and (10, 8)? (a) (12, 24) (b) (6, 12) (c) (4, 4) (d) (12, 6)
39. 39.What is the midpoint of the line joining (10, 8) and (16, 6)? (a) (7, 13) (b) (26, 14) (c) (3, 1) (d) (13, 7)
40. 40.What is the distance between the points (9, 7) and (17, 13)? (a) 14 (b) 11 (c) 100 (d) 10

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