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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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