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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 509 · 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, 21) and (13, 6)? (a) 18 (b) 289 (c) 17 (d) 23
  2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  3. 3.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  4. 4.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  5. 5.What is the midpoint of the line joining (7, 1) and (13, 7)? (a) (10, 4) (b) (4, 10) (c) (3, 3) (d) (20, 8)
  6. 6.In which quadrant does the point (−7, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  7. 7.What is the distance between the points (5, 6) and (9, 3)? (a) 6 (b) 7 (c) 5 (d) 25
  8. 8.What is the distance between the points (1, 1) and (6, 13)? (a) 169 (b) 13 (c) 17 (d) 14
  9. 9.In which quadrant does the point (6, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  10. 10.In which quadrant does the point (−7, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  11. 11.In which quadrant does the point (−3, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  12. 12.What is the midpoint of the line joining (5, 14) and (7, 6)? (a) (1, 4) (b) (12, 20) (c) (6, 10) (d) (10, 6)
  13. 13.In which quadrant does the point (6, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  14. 14.What is the midpoint of the line joining (4, 8) and (12, 0)? (a) (4, 8) (b) (8, 4) (c) (4, 4) (d) (16, 8)
  15. 15.In which quadrant does the point (−7, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  16. 16.In which quadrant does the point (−2, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  17. 17.In which quadrant does the point (−4, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  18. 18.What is the midpoint of the line joining (0, 8) and (10, 12)? (a) (5, 2) (b) (10, 20) (c) (10, 5) (d) (5, 10)
  19. 19.What is the distance between the points (9, 9) and (21, 25)? (a) 20 (b) 28 (c) 400 (d) 21
  20. 20.What is the distance between the points (0, 5) and (5, 17)? (a) 17 (b) 13 (c) 169 (d) 14
  21. 21.What is the distance between the points (2, 22) and (10, 7)? (a) 23 (b) 289 (c) 18 (d) 17
  22. 22.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  23. 23.In which quadrant does the point (6, 7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  24. 24.What is the midpoint of the line joining (0, 6) and (2, 14)? (a) (2, 20) (b) (1, 4) (c) (1, 10) (d) (10, 1)
  25. 25.What is the distance between the points (3, 9) and (15, 18)? (a) 225 (b) 15 (c) 16 (d) 21
  26. 26.What is the distance between the points (7, 7) and (12, 19)? (a) 17 (b) 13 (c) 169 (d) 14
  27. 27.What is the midpoint of the line joining (0, 5) and (10, 7)? (a) (6, 5) (b) (5, 1) (c) (10, 12) (d) (5, 6)
  28. 28.In which quadrant does the point (8, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  29. 29.What is the midpoint of the line joining (0, 5) and (2, 9)? (a) (2, 14) (b) (1, 7) (c) (7, 1) (d) (1, 2)
  30. 30.In which quadrant does the point (7, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  31. 31.What is the distance between the points (2, 18) and (10, 3)? (a) 289 (b) 23 (c) 18 (d) 17
  32. 32.What is the midpoint of the line joining (5, 7) and (7, 13)? (a) (6, 10) (b) (10, 6) (c) (1, 3) (d) (12, 20)
  33. 33.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 625 (d) 25
  34. 34.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  35. 35.What is the midpoint of the line joining (0, 3) and (6, 1)? (a) (2, 3) (b) (3, 1) (c) (3, 2) (d) (6, 4)
  36. 36.What is the distance between the points (7, 12) and (19, 3)? (a) 15 (b) 225 (c) 16 (d) 21
  37. 37.What is the distance between the points (6, 27) and (13, 3)? (a) 625 (b) 26 (c) 31 (d) 25
  38. 38.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  39. 39.What is the distance between the points (9, 4) and (12, 8)? (a) 5 (b) 25 (c) 7 (d) 6
  40. 40.In which quadrant does the point (9, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant

Answer key

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

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