Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 906 · 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, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
2. 2.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
4. 4.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
5. 5.What is the distance between the points (2, 20) and (14, 4)? (a) 20 (b) 21 (c) 400 (d) 28
6. 6.What is the distance between the points (3, 4) and (7, 1)? (a) 5 (b) 25 (c) 6 (d) 7
7. 7.In which quadrant does the point (−9, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
8. 8.What is the midpoint of the line joining (2, 9) and (12, 7)? (a) (8, 7) (b) (14, 16) (c) (5, 1) (d) (7, 8)
9. 9.In which quadrant does the point (8, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
10. 10.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
11. 11.What is the distance between the points (6, 8) and (30, 1)? (a) 25 (b) 625 (c) 26 (d) 31
12. 12.What is the distance between the points (9, 5) and (21, 0)? (a) 169 (b) 14 (c) 13 (d) 17
13. 13.What is the midpoint of the line joining (0, 11) and (4, 7)? (a) (9, 2) (b) (4, 18) (c) (2, 2) (d) (2, 9)
14. 14.In which quadrant does the point (8, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
15. 15.In which quadrant does the point (3, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
16. 16.What is the distance between the points (5, 9) and (10, 21)? (a) 169 (b) 17 (c) 13 (d) 14
17. 17.In which quadrant does the point (−7, 8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
18. 18.What is the midpoint of the line joining (0, 1) and (10, 11)? (a) (5, 6) (b) (6, 5) (c) (10, 12) (d) (5, 5)
19. 19.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
20. 20.What is the midpoint of the line joining (6, 1) and (14, 3)? (a) (20, 4) (b) (4, 1) (c) (10, 2) (d) (2, 10)
21. 21.What is the midpoint of the line joining (5, 13) and (13, 5)? (a) (4, 4) (b) (9, 9) (c) (10, 9) (d) (18, 18)
22. 22.In which quadrant does the point (−7, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
23. 23.What is the midpoint of the line joining (9, 10) and (21, 12)? (a) (6, 1) (b) (11, 15) (c) (15, 11) (d) (30, 22)
24. 24.What is the midpoint of the line joining (4, 5) and (6, 1)? (a) (1, 2) (b) (3, 5) (c) (10, 6) (d) (5, 3)
25. 25.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
26. 26.What is the distance between the points (0, 9) and (8, 15)? (a) 14 (b) 11 (c) 10 (d) 100
27. 27.What is the midpoint of the line joining (2, 9) and (4, 17)? (a) (1, 4) (b) (3, 13) (c) (13, 3) (d) (6, 26)
28. 28.What is the midpoint of the line joining (7, 13) and (17, 7)? (a) (24, 20) (b) (10, 12) (c) (12, 10) (d) (5, 3)
29. 29.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
30. 30.What is the midpoint of the line joining (0, 3) and (12, 9)? (a) (6, 6) (b) (12, 12) (c) (7, 6) (d) (6, 3)
31. 31.What is the distance between the points (8, 1) and (20, 6)? (a) 17 (b) 169 (c) 14 (d) 13
32. 32.In which quadrant does the point (−8, −5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
33. 33.What is the midpoint of the line joining (0, 7) and (4, 11)? (a) (2, 9) (b) (4, 18) (c) (9, 2) (d) (2, 2)
34. 34.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
35. 35.In which quadrant does the point (7, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
36. 36.What is the midpoint of the line joining (0, 20) and (2, 10)? (a) (15, 1) (b) (1, 5) (c) (1, 15) (d) (2, 30)
37. 37.What is the distance between the points (6, 2) and (13, 26)? (a) 26 (b) 25 (c) 625 (d) 31
38. 38.What is the midpoint of the line joining (7, 0) and (11, 2)? (a) (1, 9) (b) (18, 2) (c) (9, 1) (d) (2, 1)
39. 39.What is the distance between the points (2, 1) and (10, 16)? (a) 23 (b) 17 (c) 18 (d) 289
40. 40.What is the distance between the points (7, 0) and (15, 15)? (a) 23 (b) 18 (c) 17 (d) 289

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