Coordinate Geometry Worksheet for Maths Olympiad

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

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