Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 462 · 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 (5, 6) and (15, 0)? (a) (5, 3) (b) (10, 3) (c) (3, 10) (d) (20, 6)
2. 2.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
3. 3.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
4. 4.What is the midpoint of the line joining (7, 8) and (17, 16)? (a) (5, 4) (b) (12, 12) (c) (13, 12) (d) (24, 24)
5. 5.In which quadrant does the point (−1, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
6. 6.What is the distance between the points (6, 4) and (14, 19)? (a) 18 (b) 17 (c) 289 (d) 23
7. 7.What is the distance between the points (1, 0) and (7, 8)? (a) 14 (b) 11 (c) 10 (d) 100
8. 8.What is the midpoint of the line joining (7, 8) and (19, 10)? (a) (9, 13) (b) (6, 1) (c) (26, 18) (d) (13, 9)
9. 9.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
10. 10.What is the distance between the points (7, 17) and (19, 1)? (a) 28 (b) 21 (c) 20 (d) 400
11. 11.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
12. 12.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
13. 13.In which quadrant does the point (−1, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
14. 14.What is the distance between the points (5, 2) and (14, 14)? (a) 225 (b) 21 (c) 15 (d) 16
15. 15.What is the distance between the points (4, 0) and (20, 12)? (a) 28 (b) 21 (c) 20 (d) 400
16. 16.What is the midpoint of the line joining (9, 15) and (21, 9)? (a) (6, 3) (b) (30, 24) (c) (12, 15) (d) (15, 12)
17. 17.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 169 (d) 13
18. 18.What is the distance between the points (9, 5) and (12, 1)? (a) 25 (b) 7 (c) 6 (d) 5
19. 19.In which quadrant does the point (−9, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
20. 20.What is the midpoint of the line joining (1, 13) and (5, 5)? (a) (3, 9) (b) (2, 4) (c) (6, 18) (d) (9, 3)
21. 21.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
22. 22.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
23. 23.In which quadrant does the point (−5, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
24. 24.What is the distance between the points (0, 6) and (15, 14)? (a) 23 (b) 289 (c) 17 (d) 18
25. 25.What is the distance between the points (4, 3) and (11, 27)? (a) 625 (b) 25 (c) 31 (d) 26
26. 26.What is the midpoint of the line joining (1, 2) and (3, 6)? (a) (1, 2) (b) (4, 8) (c) (4, 2) (d) (2, 4)
27. 27.What is the midpoint of the line joining (5, 11) and (7, 1)? (a) (12, 12) (b) (7, 6) (c) (6, 6) (d) (1, 5)
28. 28.What is the midpoint of the line joining (6, 10) and (12, 0)? (a) (5, 9) (b) (9, 5) (c) (18, 10) (d) (3, 5)
29. 29.What is the midpoint of the line joining (10, 11) and (14, 7)? (a) (12, 9) (b) (24, 18) (c) (9, 12) (d) (2, 2)
30. 30.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
31. 31.In which quadrant does the point (2, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
32. 32.What is the distance between the points (5, 28) and (12, 4)? (a) 31 (b) 625 (c) 26 (d) 25
33. 33.What is the distance between the points (5, 13) and (10, 1)? (a) 13 (b) 17 (c) 169 (d) 14
34. 34.What is the midpoint of the line joining (9, 17) and (17, 9)? (a) (4, 4) (b) (26, 26) (c) (14, 13) (d) (13, 13)
35. 35.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
36. 36.What is the midpoint of the line joining (2, 9) and (6, 21)? (a) (2, 6) (b) (4, 15) (c) (8, 30) (d) (15, 4)
37. 37.What is the midpoint of the line joining (0, 1) and (4, 3)? (a) (2, 2) (b) (3, 2) (c) (4, 4) (d) (2, 1)
38. 38.In which quadrant does the point (2, −8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
39. 39.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
40. 40.In which quadrant does the point (9, −9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant

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