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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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