Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 792 · 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 (1, 14) and (11, 4)? (a) (9, 6) (b) (12, 18) (c) (5, 5) (d) (6, 9)
2. 2.In which quadrant does the point (3, −6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
3. 3.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
4. 4.What is the midpoint of the line joining (9, 1) and (13, 5)? (a) (3, 11) (b) (11, 3) (c) (22, 6) (d) (2, 2)
5. 5.What is the distance between the points (6, 2) and (18, 7)? (a) 14 (b) 13 (c) 17 (d) 169
6. 6.What is the midpoint of the line joining (1, 0) and (3, 10)? (a) (5, 2) (b) (4, 10) (c) (2, 5) (d) (1, 5)
7. 7.In which quadrant does the point (−4, −2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
8. 8.What is the distance between the points (4, 2) and (13, 14)? (a) 21 (b) 225 (c) 15 (d) 16
9. 9.What is the midpoint of the line joining (9, 12) and (13, 6)? (a) (9, 11) (b) (2, 3) (c) (22, 18) (d) (11, 9)
10. 10.What is the distance between the points (7, 0) and (10, 4)? (a) 5 (b) 7 (c) 6 (d) 25
11. 11.What is the distance between the points (8, 16) and (17, 4)? (a) 225 (b) 16 (c) 21 (d) 15
12. 12.In which quadrant does the point (2, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
13. 13.What is the distance between the points (7, 9) and (31, 16)? (a) 25 (b) 31 (c) 625 (d) 26
14. 14.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
15. 15.What is the distance between the points (0, 7) and (5, 19)? (a) 14 (b) 13 (c) 169 (d) 17
16. 16.In which quadrant does the point (3, −9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
17. 17.What is the midpoint of the line joining (2, 4) and (4, 16)? (a) (10, 3) (b) (3, 10) (c) (6, 20) (d) (1, 6)
18. 18.What is the distance between the points (2, 16) and (26, 9)? (a) 26 (b) 25 (c) 625 (d) 31
19. 19.What is the distance between the points (6, 5) and (14, 11)? (a) 11 (b) 100 (c) 10 (d) 14
20. 20.What is the midpoint of the line joining (4, 12) and (12, 6)? (a) (8, 9) (b) (16, 18) (c) (4, 3) (d) (9, 8)
21. 21.What is the midpoint of the line joining (5, 19) and (15, 7)? (a) (5, 6) (b) (20, 26) (c) (10, 13) (d) (13, 10)
22. 22.What is the distance between the points (7, 9) and (22, 17)? (a) 18 (b) 17 (c) 23 (d) 289
23. 23.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
24. 24.What is the midpoint of the line joining (2, 8) and (10, 10)? (a) (12, 18) (b) (6, 9) (c) (4, 1) (d) (9, 6)
25. 25.What is the midpoint of the line joining (1, 2) and (11, 6)? (a) (12, 8) (b) (4, 6) (c) (5, 2) (d) (6, 4)
26. 26.What is the distance between the points (2, 13) and (10, 7)? (a) 11 (b) 10 (c) 14 (d) 100
27. 27.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
28. 28.What is the distance between the points (4, 15) and (12, 9)? (a) 100 (b) 14 (c) 11 (d) 10
29. 29.What is the distance between the points (3, 6) and (12, 18)? (a) 16 (b) 15 (c) 225 (d) 21
30. 30.What is the distance between the points (1, 18) and (6, 6)? (a) 169 (b) 17 (c) 14 (d) 13
31. 31.In which quadrant does the point (4, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
32. 32.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
33. 33.In which quadrant does the point (1, 4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
34. 34.What is the midpoint of the line joining (1, 16) and (3, 4)? (a) (1, 6) (b) (2, 10) (c) (4, 20) (d) (10, 2)
35. 35.What is the midpoint of the line joining (0, 7) and (6, 5)? (a) (3, 1) (b) (6, 3) (c) (3, 6) (d) (6, 12)
36. 36.In which quadrant does the point (9, −6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
37. 37.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
38. 38.In which quadrant does the point (9, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
39. 39.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
40. 40.What is the distance between the points (1, 3) and (8, 27)? (a) 26 (b) 31 (c) 625 (d) 25

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