Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 911 · 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, 7) and (9, 15)? (a) (11, 6) (b) (12, 22) (c) (6, 11) (d) (3, 4)
2. 2.What is the midpoint of the line joining (3, 14) and (11, 10)? (a) (14, 24) (b) (4, 2) (c) (7, 12) (d) (12, 7)
3. 3.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
4. 4.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
5. 5.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
6. 6.What is the midpoint of the line joining (4, 4) and (12, 6)? (a) (5, 8) (b) (8, 5) (c) (16, 10) (d) (4, 1)
7. 7.In which quadrant does the point (−5, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
8. 8.What is the distance between the points (9, 6) and (12, 2)? (a) 6 (b) 25 (c) 5 (d) 7
9. 9.What is the distance between the points (8, 0) and (16, 15)? (a) 17 (b) 23 (c) 18 (d) 289
10. 10.What is the distance between the points (9, 17) and (21, 1)? (a) 28 (b) 400 (c) 21 (d) 20
11. 11.What is the distance between the points (2, 3) and (5, 7)? (a) 25 (b) 7 (c) 6 (d) 5
12. 12.In which quadrant does the point (4, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
13. 13.What is the midpoint of the line joining (7, 7) and (19, 5)? (a) (6, 1) (b) (6, 13) (c) (13, 6) (d) (26, 12)
14. 14.In which quadrant does the point (−9, −1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
15. 15.What is the midpoint of the line joining (8, 1) and (12, 3)? (a) (20, 4) (b) (2, 1) (c) (10, 2) (d) (2, 10)
16. 16.What is the midpoint of the line joining (10, 10) and (20, 20)? (a) (30, 30) (b) (5, 5) (c) (16, 15) (d) (15, 15)
17. 17.What is the distance between the points (1, 18) and (13, 9)? (a) 15 (b) 21 (c) 225 (d) 16
18. 18.What is the midpoint of the line joining (1, 16) and (7, 8)? (a) (4, 12) (b) (12, 4) (c) (8, 24) (d) (3, 4)
19. 19.What is the midpoint of the line joining (9, 4) and (17, 6)? (a) (5, 13) (b) (26, 10) (c) (13, 5) (d) (4, 1)
20. 20.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
21. 21.What is the distance between the points (4, 25) and (11, 1)? (a) 31 (b) 25 (c) 625 (d) 26
22. 22.In which quadrant does the point (−6, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
23. 23.What is the midpoint of the line joining (2, 13) and (12, 9)? (a) (11, 7) (b) (7, 11) (c) (14, 22) (d) (5, 2)
24. 24.What is the distance between the points (9, 2) and (21, 18)? (a) 28 (b) 20 (c) 400 (d) 21
25. 25.What is the distance between the points (4, 9) and (7, 13)? (a) 7 (b) 25 (c) 6 (d) 5
26. 26.What is the distance between the points (2, 6) and (26, 13)? (a) 25 (b) 625 (c) 31 (d) 26
27. 27.In which quadrant does the point (5, 7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
28. 28.What is the midpoint of the line joining (6, 2) and (18, 10)? (a) (6, 12) (b) (12, 6) (c) (6, 4) (d) (24, 12)
29. 29.What is the distance between the points (6, 16) and (11, 4)? (a) 17 (b) 14 (c) 169 (d) 13
30. 30.In which quadrant does the point (4, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
31. 31.In which quadrant does the point (−4, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
32. 32.What is the distance between the points (3, 12) and (8, 0)? (a) 13 (b) 17 (c) 14 (d) 169
33. 33.What is the midpoint of the line joining (4, 14) and (14, 2)? (a) (9, 8) (b) (8, 9) (c) (18, 16) (d) (5, 6)
34. 34.What is the midpoint of the line joining (0, 5) and (2, 3)? (a) (4, 1) (b) (1, 4) (c) (2, 8) (d) (1, 1)
35. 35.What is the distance between the points (3, 14) and (27, 7)? (a) 625 (b) 31 (c) 26 (d) 25
36. 36.What is the midpoint of the line joining (0, 17) and (6, 5)? (a) (3, 6) (b) (11, 3) (c) (6, 22) (d) (3, 11)
37. 37.In which quadrant does the point (6, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
38. 38.In which quadrant does the point (3, 3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
39. 39.In which quadrant does the point (1, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
40. 40.What is the midpoint of the line joining (2, 4) and (6, 10)? (a) (4, 7) (b) (7, 4) (c) (8, 14) (d) (2, 3)

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