Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 140 · 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 (1, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
2. 2.What is the midpoint of the line joining (10, 12) and (16, 6)? (a) (9, 13) (b) (3, 3) (c) (13, 9) (d) (26, 18)
3. 3.What is the midpoint of the line joining (1, 18) and (11, 6)? (a) (12, 6) (b) (12, 24) (c) (5, 6) (d) (6, 12)
4. 4.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
5. 5.In which quadrant does the point (−1, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
6. 6.In which quadrant does the point (3, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
7. 7.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
8. 8.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
9. 9.In which quadrant does the point (−6, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
10. 10.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
11. 11.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
12. 12.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
13. 13.What is the distance between the points (2, 12) and (11, 0)? (a) 16 (b) 21 (c) 15 (d) 225
14. 14.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
15. 15.What is the distance between the points (6, 4) and (11, 16)? (a) 14 (b) 17 (c) 169 (d) 13
16. 16.What is the midpoint of the line joining (4, 1) and (10, 7)? (a) (3, 3) (b) (14, 8) (c) (7, 4) (d) (4, 7)
17. 17.In which quadrant does the point (−1, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
18. 18.What is the distance between the points (0, 8) and (15, 16)? (a) 17 (b) 23 (c) 289 (d) 18
19. 19.In which quadrant does the point (−7, 3) 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, 9)? (a) (11, 5) (b) (5, 11) (c) (10, 22) (d) (1, 2)
21. 21.What is the distance between the points (0, 12) and (4, 9)? (a) 5 (b) 7 (c) 25 (d) 6
22. 22.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
23. 23.What is the midpoint of the line joining (10, 12) and (12, 4)? (a) (22, 16) (b) (11, 8) (c) (1, 4) (d) (8, 11)
24. 24.What is the midpoint of the line joining (7, 0) and (15, 2)? (a) (1, 11) (b) (4, 1) (c) (22, 2) (d) (11, 1)
25. 25.What is the midpoint of the line joining (8, 11) and (12, 3)? (a) (2, 4) (b) (10, 7) (c) (20, 14) (d) (7, 10)
26. 26.In which quadrant does the point (−5, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
27. 27.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
28. 28.In which quadrant does the point (2, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
29. 29.What is the midpoint of the line joining (7, 2) and (17, 10)? (a) (6, 12) (b) (24, 12) (c) (12, 6) (d) (5, 4)
30. 30.In which quadrant does the point (−4, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
31. 31.What is the midpoint of the line joining (0, 6) and (2, 8)? (a) (2, 14) (b) (7, 1) (c) (1, 7) (d) (1, 1)
32. 32.What is the distance between the points (0, 7) and (12, 12)? (a) 17 (b) 14 (c) 169 (d) 13
33. 33.In which quadrant does the point (−9, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
34. 34.What is the distance between the points (5, 3) and (9, 0)? (a) 6 (b) 5 (c) 7 (d) 25
35. 35.What is the midpoint of the line joining (0, 9) and (8, 21)? (a) (4, 15) (b) (4, 6) (c) (15, 4) (d) (8, 30)
36. 36.In which quadrant does the point (3, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
37. 37.What is the distance between the points (0, 4) and (8, 10)? (a) 14 (b) 100 (c) 11 (d) 10
38. 38.In which quadrant does the point (2, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
39. 39.In which quadrant does the point (−3, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
40. 40.What is the distance between the points (4, 4) and (20, 16)? (a) 21 (b) 28 (c) 400 (d) 20

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