Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 134 · 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, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
2. 2.What is the midpoint of the line joining (6, 3) and (10, 7)? (a) (8, 5) (b) (5, 8) (c) (2, 2) (d) (16, 10)
3. 3.What is the distance between the points (0, 16) and (6, 8)? (a) 10 (b) 14 (c) 11 (d) 100
4. 4.What is the distance between the points (1, 0) and (13, 5)? (a) 13 (b) 17 (c) 14 (d) 169
5. 5.What is the distance between the points (8, 23) and (20, 7)? (a) 20 (b) 400 (c) 21 (d) 28
6. 6.What is the midpoint of the line joining (9, 0) and (19, 2)? (a) (1, 14) (b) (5, 1) (c) (28, 2) (d) (14, 1)
7. 7.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
8. 8.What is the distance between the points (3, 21) and (19, 9)? (a) 20 (b) 28 (c) 21 (d) 400
9. 9.What is the midpoint of the line joining (5, 5) and (7, 17)? (a) (6, 11) (b) (11, 6) (c) (1, 6) (d) (12, 22)
10. 10.What is the distance between the points (5, 9) and (17, 25)? (a) 28 (b) 400 (c) 21 (d) 20
11. 11.What is the distance between the points (4, 3) and (16, 19)? (a) 20 (b) 400 (c) 28 (d) 21
12. 12.In which quadrant does the point (5, −2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
13. 13.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
14. 14.What is the midpoint of the line joining (3, 9) and (5, 11)? (a) (10, 4) (b) (4, 10) (c) (1, 1) (d) (8, 20)
15. 15.What is the midpoint of the line joining (9, 6) and (15, 2)? (a) (4, 12) (b) (12, 4) (c) (24, 8) (d) (3, 2)
16. 16.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
17. 17.In which quadrant does the point (8, 3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
18. 18.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 28 (d) 21
19. 19.What is the midpoint of the line joining (2, 2) and (10, 12)? (a) (7, 6) (b) (4, 5) (c) (6, 7) (d) (12, 14)
20. 20.What is the distance between the points (2, 3) and (6, 0)? (a) 25 (b) 5 (c) 7 (d) 6
21. 21.What is the midpoint of the line joining (6, 7) and (16, 5)? (a) (22, 12) (b) (5, 1) (c) (11, 6) (d) (6, 11)
22. 22.What is the midpoint of the line joining (9, 2) and (17, 4)? (a) (4, 1) (b) (13, 3) (c) (3, 13) (d) (26, 6)
23. 23.What is the distance between the points (7, 2) and (19, 11)? (a) 225 (b) 21 (c) 15 (d) 16
24. 24.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
25. 25.What is the midpoint of the line joining (9, 8) and (17, 6)? (a) (26, 14) (b) (13, 7) (c) (4, 1) (d) (7, 13)
26. 26.What is the midpoint of the line joining (7, 5) and (13, 15)? (a) (20, 20) (b) (10, 10) (c) (3, 5) (d) (11, 10)
27. 27.What is the midpoint of the line joining (9, 20) and (19, 8)? (a) (15, 14) (b) (28, 28) (c) (5, 6) (d) (14, 14)
28. 28.What is the distance between the points (9, 0) and (16, 24)? (a) 625 (b) 31 (c) 26 (d) 25
29. 29.What is the midpoint of the line joining (8, 8) and (10, 6)? (a) (7, 9) (b) (18, 14) (c) (9, 7) (d) (1, 1)
30. 30.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
31. 31.What is the midpoint of the line joining (8, 10) and (18, 16)? (a) (13, 13) (b) (14, 13) (c) (26, 26) (d) (5, 3)
32. 32.What is the distance between the points (1, 9) and (10, 21)? (a) 21 (b) 15 (c) 225 (d) 16
33. 33.In which quadrant does the point (8, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
34. 34.What is the distance between the points (2, 2) and (5, 6)? (a) 6 (b) 25 (c) 5 (d) 7
35. 35.What is the distance between the points (8, 0) and (12, 3)? (a) 5 (b) 7 (c) 25 (d) 6
36. 36.What is the midpoint of the line joining (1, 6) and (13, 2)? (a) (7, 4) (b) (6, 2) (c) (14, 8) (d) (4, 7)
37. 37.What is the distance between the points (4, 7) and (19, 15)? (a) 18 (b) 23 (c) 17 (d) 289
38. 38.In which quadrant does the point (6, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
39. 39.What is the distance between the points (1, 8) and (9, 23)? (a) 23 (b) 17 (c) 18 (d) 289
40. 40.In which quadrant does the point (3, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant

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