Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 442 · 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.In which quadrant does the point (−8, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
2. 2.In which quadrant does the point (2, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
3. 3.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
4. 4.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
5. 5.What is the midpoint of the line joining (0, 0) and (12, 10)? (a) (5, 6) (b) (7, 5) (c) (6, 5) (d) (12, 10)
6. 6.What is the midpoint of the line joining (2, 8) and (8, 2)? (a) (5, 5) (b) (10, 10) (c) (3, 3) (d) (6, 5)
7. 7.In which quadrant does the point (6, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
8. 8.In which quadrant does the point (−4, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
9. 9.In which quadrant does the point (7, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
10. 10.In which quadrant does the point (6, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
11. 11.In which quadrant does the point (−2, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
12. 12.What is the midpoint of the line joining (5, 4) and (17, 6)? (a) (6, 1) (b) (22, 10) (c) (5, 11) (d) (11, 5)
13. 13.What is the midpoint of the line joining (0, 7) and (2, 5)? (a) (6, 1) (b) (2, 12) (c) (1, 6) (d) (1, 1)
14. 14.In which quadrant does the point (1, −6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
15. 15.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
16. 16.What is the distance between the points (6, 24) and (14, 9)? (a) 18 (b) 289 (c) 23 (d) 17
17. 17.In which quadrant does the point (−9, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
18. 18.What is the distance between the points (7, 17) and (15, 2)? (a) 18 (b) 23 (c) 289 (d) 17
19. 19.In which quadrant does the point (2, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
20. 20.What is the midpoint of the line joining (8, 17) and (20, 7)? (a) (6, 5) (b) (12, 14) (c) (28, 24) (d) (14, 12)
21. 21.What is the distance between the points (0, 4) and (12, 9)? (a) 13 (b) 14 (c) 169 (d) 17
22. 22.In which quadrant does the point (−2, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
23. 23.What is the midpoint of the line joining (1, 6) and (3, 18)? (a) (2, 12) (b) (4, 24) (c) (1, 6) (d) (12, 2)
24. 24.What is the distance between the points (3, 5) and (9, 13)? (a) 100 (b) 14 (c) 10 (d) 11
25. 25.What is the distance between the points (9, 15) and (15, 7)? (a) 14 (b) 11 (c) 10 (d) 100
26. 26.What is the midpoint of the line joining (1, 2) and (11, 4)? (a) (12, 6) (b) (3, 6) (c) (6, 3) (d) (5, 1)
27. 27.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 6 (d) 25
28. 28.What is the distance between the points (9, 21) and (18, 9)? (a) 16 (b) 15 (c) 21 (d) 225
29. 29.What is the midpoint of the line joining (0, 13) and (12, 5)? (a) (12, 18) (b) (9, 6) (c) (6, 4) (d) (6, 9)
30. 30.What is the midpoint of the line joining (10, 6) and (22, 0)? (a) (6, 3) (b) (16, 3) (c) (3, 16) (d) (32, 6)
31. 31.In which quadrant does the point (−8, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
32. 32.In which quadrant does the point (−3, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
33. 33.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 21 (d) 16
34. 34.In which quadrant does the point (−6, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
35. 35.What is the distance between the points (5, 2) and (29, 9)? (a) 25 (b) 26 (c) 625 (d) 31
36. 36.What is the midpoint of the line joining (1, 0) and (13, 2)? (a) (6, 1) (b) (7, 1) (c) (14, 2) (d) (1, 7)
37. 37.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
38. 38.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
39. 39.In which quadrant does the point (9, −8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
40. 40.What is the distance between the points (1, 0) and (5, 3)? (a) 7 (b) 25 (c) 6 (d) 5

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