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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 904 · 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 (5, 0) and (8, 4)? (a) 6 (b) 25 (c) 7 (d) 5
  2. 2.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  3. 3.What is the distance between the points (6, 4) and (12, 12)? (a) 11 (b) 100 (c) 14 (d) 10
  4. 4.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  5. 5.What is the distance between the points (8, 13) and (24, 1)? (a) 400 (b) 21 (c) 20 (d) 28
  6. 6.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
  7. 7.What is the distance between the points (8, 9) and (15, 33)? (a) 625 (b) 26 (c) 31 (d) 25
  8. 8.What is the distance between the points (8, 13) and (11, 9)? (a) 7 (b) 5 (c) 6 (d) 25
  9. 9.What is the distance between the points (8, 2) and (15, 26)? (a) 26 (b) 625 (c) 31 (d) 25
  10. 10.What is the distance between the points (3, 12) and (7, 9)? (a) 5 (b) 25 (c) 6 (d) 7
  11. 11.What is the distance between the points (4, 16) and (16, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  12. 12.What is the distance between the points (9, 16) and (24, 8)? (a) 289 (b) 18 (c) 23 (d) 17
  13. 13.What is the midpoint of the line joining (7, 5) and (13, 13)? (a) (10, 9) (b) (3, 4) (c) (9, 10) (d) (20, 18)
  14. 14.In which quadrant does the point (4, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  15. 15.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
  16. 16.What is the distance between the points (6, 25) and (13, 1)? (a) 625 (b) 31 (c) 25 (d) 26
  17. 17.In which quadrant does the point (8, −1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  18. 18.What is the distance between the points (6, 1) and (21, 9)? (a) 17 (b) 289 (c) 23 (d) 18
  19. 19.In which quadrant does the point (−6, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  20. 20.In which quadrant does the point (−1, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  21. 21.In which quadrant does the point (1, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  22. 22.What is the distance between the points (8, 8) and (12, 5)? (a) 6 (b) 25 (c) 5 (d) 7
  23. 23.In which quadrant does the point (6, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  24. 24.In which quadrant does the point (3, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  25. 25.What is the midpoint of the line joining (5, 8) and (9, 2)? (a) (2, 3) (b) (14, 10) (c) (7, 5) (d) (5, 7)
  26. 26.In which quadrant does the point (−1, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  27. 27.What is the midpoint of the line joining (0, 10) and (4, 16)? (a) (13, 2) (b) (2, 3) (c) (2, 13) (d) (4, 26)
  28. 28.What is the distance between the points (1, 23) and (9, 8)? (a) 289 (b) 17 (c) 23 (d) 18
  29. 29.What is the midpoint of the line joining (5, 7) and (7, 3)? (a) (12, 10) (b) (5, 6) (c) (1, 2) (d) (6, 5)
  30. 30.What is the distance between the points (6, 18) and (18, 9)? (a) 21 (b) 16 (c) 15 (d) 225
  31. 31.What is the distance between the points (4, 3) and (8, 6)? (a) 5 (b) 6 (c) 25 (d) 7
  32. 32.In which quadrant does the point (1, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  33. 33.In which quadrant does the point (3, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  34. 34.What is the distance between the points (4, 15) and (19, 7)? (a) 23 (b) 289 (c) 18 (d) 17
  35. 35.In which quadrant does the point (3, 5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  36. 36.What is the midpoint of the line joining (9, 9) and (13, 11)? (a) (10, 11) (b) (22, 20) (c) (11, 10) (d) (2, 1)
  37. 37.What is the distance between the points (3, 0) and (11, 6)? (a) 10 (b) 14 (c) 11 (d) 100
  38. 38.What is the distance between the points (4, 7) and (7, 11)? (a) 25 (b) 5 (c) 6 (d) 7
  39. 39.What is the midpoint of the line joining (10, 14) and (20, 4)? (a) (30, 18) (b) (5, 5) (c) (9, 15) (d) (15, 9)
  40. 40.What is the midpoint of the line joining (8, 4) and (12, 0)? (a) (10, 2) (b) (2, 10) (c) (2, 2) (d) (20, 4)

Answer key

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

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