Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 647 · 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 (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
2. 2.What is the midpoint of the line joining (6, 10) and (16, 6)? (a) (8, 11) (b) (22, 16) (c) (11, 8) (d) (5, 2)
3. 3.What is the midpoint of the line joining (2, 9) and (6, 11)? (a) (10, 4) (b) (8, 20) (c) (4, 10) (d) (2, 1)
4. 4.What is the distance between the points (6, 8) and (15, 20)? (a) 15 (b) 21 (c) 225 (d) 16
5. 5.What is the distance between the points (5, 5) and (14, 17)? (a) 16 (b) 225 (c) 15 (d) 21
6. 6.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
7. 7.What is the midpoint of the line joining (4, 16) and (10, 8)? (a) (12, 7) (b) (3, 4) (c) (14, 24) (d) (7, 12)
8. 8.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
9. 9.What is the distance between the points (7, 2) and (16, 14)? (a) 21 (b) 16 (c) 225 (d) 15
10. 10.What is the midpoint of the line joining (2, 2) and (8, 4)? (a) (10, 6) (b) (3, 1) (c) (3, 5) (d) (5, 3)
11. 11.What is the midpoint of the line joining (2, 9) and (8, 21)? (a) (5, 15) (b) (3, 6) (c) (10, 30) (d) (15, 5)
12. 12.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
13. 13.In which quadrant does the point (−1, −1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
14. 14.What is the midpoint of the line joining (8, 9) and (14, 5)? (a) (3, 2) (b) (22, 14) (c) (7, 11) (d) (11, 7)
15. 15.In which quadrant does the point (8, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
16. 16.What is the distance between the points (0, 16) and (24, 9)? (a) 25 (b) 625 (c) 26 (d) 31
17. 17.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
18. 18.In which quadrant does the point (5, 8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
19. 19.In which quadrant does the point (−4, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
20. 20.What is the midpoint of the line joining (10, 20) and (12, 10)? (a) (15, 11) (b) (11, 15) (c) (1, 5) (d) (22, 30)
21. 21.In which quadrant does the point (9, −5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
22. 22.In which quadrant does the point (−2, −2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
23. 23.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
24. 24.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
25. 25.What is the distance between the points (5, 20) and (10, 8)? (a) 13 (b) 17 (c) 14 (d) 169
26. 26.In which quadrant does the point (8, 9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
27. 27.What is the midpoint of the line joining (5, 4) and (7, 0)? (a) (12, 4) (b) (6, 2) (c) (2, 6) (d) (1, 2)
28. 28.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
29. 29.What is the distance between the points (5, 9) and (20, 17)? (a) 23 (b) 18 (c) 289 (d) 17
30. 30.What is the midpoint of the line joining (7, 11) and (19, 3)? (a) (6, 4) (b) (13, 7) (c) (7, 13) (d) (26, 14)
31. 31.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
32. 32.What is the distance between the points (2, 4) and (10, 10)? (a) 14 (b) 100 (c) 11 (d) 10
33. 33.What is the distance between the points (5, 12) and (17, 7)? (a) 17 (b) 169 (c) 14 (d) 13
34. 34.What is the midpoint of the line joining (7, 6) and (9, 12)? (a) (8, 9) (b) (16, 18) (c) (9, 8) (d) (1, 3)
35. 35.What is the midpoint of the line joining (3, 2) and (5, 4)? (a) (1, 1) (b) (3, 4) (c) (4, 3) (d) (8, 6)
36. 36.In which quadrant does the point (9, −9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
37. 37.What is the midpoint of the line joining (1, 12) and (13, 0)? (a) (14, 12) (b) (6, 6) (c) (7, 6) (d) (6, 7)
38. 38.In which quadrant does the point (8, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
39. 39.What is the distance between the points (6, 13) and (22, 1)? (a) 28 (b) 400 (c) 21 (d) 20
40. 40.What is the midpoint of the line joining (3, 11) and (13, 3)? (a) (7, 8) (b) (16, 14) (c) (8, 7) (d) (5, 4)

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