Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 542 · 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 (5, 12) and (13, 6)? (a) 11 (b) 100 (c) 10 (d) 14
2. 2.In which quadrant does the point (−4, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
3. 3.In which quadrant does the point (9, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
4. 4.What is the midpoint of the line joining (9, 7) and (21, 11)? (a) (15, 9) (b) (30, 18) (c) (6, 2) (d) (9, 15)
5. 5.In which quadrant does the point (8, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
6. 6.What is the distance between the points (0, 13) and (3, 9)? (a) 6 (b) 5 (c) 25 (d) 7
7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
8. 8.What is the distance between the points (7, 15) and (19, 6)? (a) 15 (b) 21 (c) 225 (d) 16
9. 9.What is the midpoint of the line joining (8, 0) and (10, 10)? (a) (9, 5) (b) (5, 9) (c) (1, 5) (d) (18, 10)
10. 10.In which quadrant does the point (8, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
12. 12.In which quadrant does the point (2, −7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
13. 13.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
14. 14.What is the midpoint of the line joining (4, 2) and (14, 4)? (a) (3, 9) (b) (5, 1) (c) (18, 6) (d) (9, 3)
15. 15.What is the midpoint of the line joining (9, 6) and (13, 0)? (a) (22, 6) (b) (3, 11) (c) (11, 3) (d) (2, 3)
16. 16.In which quadrant does the point (2, −6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
17. 17.What is the midpoint of the line joining (0, 12) and (6, 2)? (a) (6, 14) (b) (3, 7) (c) (7, 3) (d) (3, 5)
18. 18.What is the midpoint of the line joining (3, 10) and (7, 0)? (a) (6, 5) (b) (10, 10) (c) (5, 5) (d) (2, 5)
19. 19.In which quadrant does the point (5, 9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
20. 20.What is the midpoint of the line joining (5, 1) and (7, 9)? (a) (5, 6) (b) (1, 4) (c) (6, 5) (d) (12, 10)
21. 21.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
22. 22.What is the midpoint of the line joining (10, 8) and (14, 6)? (a) (7, 12) (b) (2, 1) (c) (12, 7) (d) (24, 14)
23. 23.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
24. 24.What is the distance between the points (7, 18) and (19, 2)? (a) 20 (b) 28 (c) 400 (d) 21
25. 25.What is the midpoint of the line joining (0, 11) and (2, 9)? (a) (1, 1) (b) (10, 1) (c) (2, 20) (d) (1, 10)
26. 26.What is the midpoint of the line joining (10, 7) and (20, 17)? (a) (15, 12) (b) (5, 5) (c) (30, 24) (d) (12, 15)
27. 27.What is the distance between the points (9, 4) and (16, 28)? (a) 26 (b) 625 (c) 31 (d) 25
28. 28.In which quadrant does the point (−1, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
29. 29.What is the midpoint of the line joining (3, 8) and (15, 14)? (a) (11, 9) (b) (6, 3) (c) (18, 22) (d) (9, 11)
30. 30.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
31. 31.What is the midpoint of the line joining (2, 0) and (12, 10)? (a) (5, 7) (b) (5, 5) (c) (14, 10) (d) (7, 5)
32. 32.What is the distance between the points (2, 9) and (7, 21)? (a) 169 (b) 13 (c) 17 (d) 14
33. 33.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
34. 34.In which quadrant does the point (−5, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
35. 35.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
36. 36.In which quadrant does the point (6, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
37. 37.What is the midpoint of the line joining (6, 4) and (8, 12)? (a) (7, 8) (b) (14, 16) (c) (1, 4) (d) (8, 7)
38. 38.What is the midpoint of the line joining (0, 12) and (4, 6)? (a) (2, 9) (b) (4, 18) (c) (9, 2) (d) (2, 3)
39. 39.What is the midpoint of the line joining (10, 6) and (16, 0)? (a) (13, 3) (b) (3, 13) (c) (3, 3) (d) (26, 6)
40. 40.What is the distance between the points (0, 0) and (5, 12)? (a) 14 (b) 169 (c) 17 (d) 13

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