← Coordinates and distance lesson New set →

Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 903 · 40 questions
TalentJR

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.

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

Answer key

  1. 10
  2. (8, 9)
  3. (6, 6)
  4. 17
  5. 10
  6. (8, 11)
  7. (1, 10)
  8. (3, 16)
  9. 13
  10. (8, 3)
  11. 10
  12. 17
  13. 25
  14. Fourth quadrant
  15. Third quadrant
  16. 5
  17. 5
  18. (6, 10)
  19. 17
  20. (11, 6)
  21. 10
  22. 10
  23. 15
  24. (15, 16)
  25. First quadrant
  26. 5
  27. (9, 11)
  28. 5
  29. 10
  30. 15
  31. 5
  32. 15
  33. (14, 11)
  34. Fourth quadrant
  35. (6, 11)
  36. 10
  37. 25
  38. 10
  39. 10
  40. Fourth quadrant

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