Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 301 · 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 (3, 4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
2. 2.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
3. 3.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
4. 4.What is the midpoint of the line joining (4, 8) and (12, 10)? (a) (4, 1) (b) (9, 8) (c) (16, 18) (d) (8, 9)
5. 5.What is the distance between the points (6, 6) and (21, 14)? (a) 23 (b) 18 (c) 289 (d) 17
6. 6.What is the distance between the points (1, 5) and (5, 2)? (a) 7 (b) 5 (c) 6 (d) 25
7. 7.What is the midpoint of the line joining (4, 10) and (16, 2)? (a) (20, 12) (b) (6, 4) (c) (6, 10) (d) (10, 6)
8. 8.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
9. 9.In which quadrant does the point (−7, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
10. 10.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
11. 11.What is the distance between the points (1, 15) and (17, 3)? (a) 400 (b) 21 (c) 28 (d) 20
12. 12.What is the distance between the points (4, 18) and (20, 6)? (a) 28 (b) 400 (c) 21 (d) 20
13. 13.What is the midpoint of the line joining (9, 5) and (21, 11)? (a) (8, 15) (b) (6, 3) (c) (15, 8) (d) (30, 16)
14. 14.What is the distance between the points (4, 30) and (11, 6)? (a) 25 (b) 625 (c) 26 (d) 31
15. 15.In which quadrant does the point (4, 7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
16. 16.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
17. 17.What is the distance between the points (3, 2) and (12, 14)? (a) 225 (b) 15 (c) 21 (d) 16
18. 18.What is the distance between the points (1, 10) and (9, 4)? (a) 11 (b) 100 (c) 10 (d) 14
19. 19.In which quadrant does the point (−5, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
20. 20.In which quadrant does the point (−8, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
21. 21.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
22. 22.What is the distance between the points (0, 5) and (8, 11)? (a) 10 (b) 14 (c) 100 (d) 11
23. 23.In which quadrant does the point (−1, −2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
24. 24.What is the midpoint of the line joining (3, 9) and (11, 21)? (a) (14, 30) (b) (15, 7) (c) (4, 6) (d) (7, 15)
25. 25.In which quadrant does the point (−1, −6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
26. 26.What is the midpoint of the line joining (7, 5) and (13, 3)? (a) (10, 4) (b) (3, 1) (c) (20, 8) (d) (4, 10)
27. 27.In which quadrant does the point (−4, 1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
28. 28.What is the midpoint of the line joining (4, 18) and (6, 10)? (a) (14, 5) (b) (10, 28) (c) (5, 14) (d) (1, 4)
29. 29.What is the distance between the points (8, 19) and (20, 3)? (a) 400 (b) 21 (c) 20 (d) 28
30. 30.What is the distance between the points (8, 16) and (14, 8)? (a) 100 (b) 11 (c) 14 (d) 10
31. 31.What is the midpoint of the line joining (0, 19) and (12, 9)? (a) (6, 5) (b) (12, 28) (c) (14, 6) (d) (6, 14)
32. 32.In which quadrant does the point (−5, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
33. 33.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
34. 34.In which quadrant does the point (7, −1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
35. 35.In which quadrant does the point (−9, −6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
36. 36.What is the midpoint of the line joining (2, 10) and (10, 12)? (a) (12, 22) (b) (11, 6) (c) (4, 1) (d) (6, 11)
37. 37.In which quadrant does the point (8, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
38. 38.What is the distance between the points (8, 7) and (13, 19)? (a) 13 (b) 14 (c) 169 (d) 17
39. 39.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
40. 40.What is the midpoint of the line joining (8, 10) and (14, 14)? (a) (12, 11) (b) (3, 2) (c) (11, 12) (d) (22, 24)

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