Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 756 · 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.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
2. 2.What is the midpoint of the line joining (3, 9) and (5, 7)? (a) (1, 1) (b) (8, 16) (c) (4, 8) (d) (8, 4)
3. 3.In which quadrant does the point (3, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
4. 4.In which quadrant does the point (8, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
5. 5.What is the distance between the points (0, 9) and (4, 6)? (a) 7 (b) 6 (c) 5 (d) 25
6. 6.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
7. 7.What is the midpoint of the line joining (3, 8) and (11, 6)? (a) (14, 14) (b) (8, 7) (c) (7, 7) (d) (4, 1)
8. 8.What is the distance between the points (4, 2) and (19, 10)? (a) 289 (b) 23 (c) 18 (d) 17
9. 9.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
10. 10.In which quadrant does the point (6, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
11. 11.What is the midpoint of the line joining (7, 15) and (9, 3)? (a) (16, 18) (b) (1, 6) (c) (8, 9) (d) (9, 8)
12. 12.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
13. 13.What is the distance between the points (2, 18) and (10, 3)? (a) 289 (b) 17 (c) 18 (d) 23
14. 14.What is the distance between the points (2, 11) and (10, 5)? (a) 10 (b) 14 (c) 11 (d) 100
15. 15.What is the distance between the points (9, 6) and (12, 2)? (a) 5 (b) 7 (c) 6 (d) 25
16. 16.What is the midpoint of the line joining (8, 1) and (14, 5)? (a) (22, 6) (b) (3, 2) (c) (3, 11) (d) (11, 3)
17. 17.What is the distance between the points (8, 9) and (20, 0)? (a) 15 (b) 16 (c) 225 (d) 21
18. 18.What is the midpoint of the line joining (10, 1) and (16, 3)? (a) (13, 2) (b) (26, 4) (c) (3, 1) (d) (2, 13)
19. 19.In which quadrant does the point (−9, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
20. 20.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
21. 21.What is the midpoint of the line joining (9, 5) and (15, 1)? (a) (3, 12) (b) (12, 3) (c) (3, 2) (d) (24, 6)
22. 22.What is the distance between the points (5, 9) and (10, 21)? (a) 13 (b) 17 (c) 14 (d) 169
23. 23.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
24. 24.What is the midpoint of the line joining (6, 10) and (12, 20)? (a) (3, 5) (b) (18, 30) (c) (9, 15) (d) (15, 9)
25. 25.In which quadrant does the point (8, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
26. 26.What is the midpoint of the line joining (0, 5) and (6, 15)? (a) (3, 5) (b) (10, 3) (c) (3, 10) (d) (6, 20)
27. 27.What is the midpoint of the line joining (9, 6) and (17, 14)? (a) (26, 20) (b) (4, 4) (c) (13, 10) (d) (10, 13)
28. 28.What is the midpoint of the line joining (6, 10) and (12, 2)? (a) (18, 12) (b) (9, 6) (c) (6, 9) (d) (3, 4)
29. 29.What is the distance between the points (7, 3) and (19, 8)? (a) 13 (b) 169 (c) 17 (d) 14
30. 30.What is the distance between the points (7, 4) and (15, 19)? (a) 289 (b) 18 (c) 17 (d) 23
31. 31.In which quadrant does the point (1, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
32. 32.In which quadrant does the point (1, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
33. 33.What is the midpoint of the line joining (9, 9) and (15, 3)? (a) (12, 6) (b) (24, 12) (c) (3, 3) (d) (6, 12)
34. 34.In which quadrant does the point (−2, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
35. 35.In which quadrant does the point (−6, −1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
36. 36.In which quadrant does the point (−1, 5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
37. 37.What is the midpoint of the line joining (6, 10) and (8, 18)? (a) (7, 14) (b) (1, 4) (c) (14, 7) (d) (14, 28)
38. 38.What is the midpoint of the line joining (8, 2) and (20, 4)? (a) (6, 1) (b) (14, 3) (c) (28, 6) (d) (3, 14)
39. 39.What is the distance between the points (1, 7) and (13, 23)? (a) 21 (b) 28 (c) 20 (d) 400
40. 40.What is the midpoint of the line joining (10, 14) and (14, 4)? (a) (9, 12) (b) (2, 5) (c) (12, 9) (d) (24, 18)

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