Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 524 · 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 distance between the points (0, 0) and (3, 4)? (a) 5 (b) 25 (c) 6 (d) 7
2. 2.In which quadrant does the point (1, 9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
3. 3.In which quadrant does the point (9, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
4. 4.In which quadrant does the point (−5, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
5. 5.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
6. 6.In which quadrant does the point (3, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
7. 7.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
8. 8.What is the distance between the points (2, 7) and (5, 11)? (a) 7 (b) 6 (c) 5 (d) 25
9. 9.In which quadrant does the point (−4, 1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
10. 10.What is the midpoint of the line joining (8, 8) and (18, 12)? (a) (5, 2) (b) (26, 20) (c) (13, 10) (d) (10, 13)
11. 11.What is the midpoint of the line joining (6, 10) and (14, 6)? (a) (4, 2) (b) (20, 16) (c) (8, 10) (d) (10, 8)
12. 12.What is the midpoint of the line joining (2, 9) and (14, 7)? (a) (8, 8) (b) (9, 8) (c) (6, 1) (d) (16, 16)
13. 13.In which quadrant does the point (−1, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
14. 14.In which quadrant does the point (−3, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
15. 15.What is the distance between the points (5, 4) and (21, 16)? (a) 400 (b) 28 (c) 20 (d) 21
16. 16.What is the midpoint of the line joining (1, 18) and (9, 6)? (a) (10, 24) (b) (5, 12) (c) (12, 5) (d) (4, 6)
17. 17.In which quadrant does the point (−4, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
18. 18.What is the distance between the points (7, 13) and (23, 1)? (a) 21 (b) 20 (c) 400 (d) 28
19. 19.What is the distance between the points (3, 16) and (15, 0)? (a) 28 (b) 21 (c) 400 (d) 20
20. 20.In which quadrant does the point (5, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
21. 21.In which quadrant does the point (3, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
22. 22.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
23. 23.What is the distance between the points (4, 2) and (10, 10)? (a) 100 (b) 14 (c) 11 (d) 10
24. 24.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
25. 25.What is the distance between the points (2, 9) and (8, 1)? (a) 10 (b) 100 (c) 11 (d) 14
26. 26.What is the midpoint of the line joining (8, 0) and (14, 8)? (a) (4, 11) (b) (3, 4) (c) (11, 4) (d) (22, 8)
27. 27.In which quadrant does the point (−6, −9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
28. 28.In which quadrant does the point (1, −9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
29. 29.What is the midpoint of the line joining (10, 11) and (16, 1)? (a) (3, 5) (b) (13, 6) (c) (6, 13) (d) (26, 12)
30. 30.In which quadrant does the point (−8, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
31. 31.In which quadrant does the point (8, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
32. 32.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
33. 33.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
34. 34.What is the midpoint of the line joining (1, 12) and (13, 2)? (a) (8, 7) (b) (7, 7) (c) (14, 14) (d) (6, 5)
35. 35.In which quadrant does the point (−6, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
36. 36.In which quadrant does the point (9, −1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
37. 37.What is the midpoint of the line joining (4, 10) and (8, 2)? (a) (6, 6) (b) (7, 6) (c) (2, 4) (d) (12, 12)
38. 38.What is the distance between the points (6, 1) and (22, 13)? (a) 21 (b) 20 (c) 28 (d) 400
39. 39.What is the distance between the points (1, 2) and (17, 14)? (a) 400 (b) 28 (c) 20 (d) 21
40. 40.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25

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