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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 187 · 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 (3, 2) and (18, 10)? (a) 17 (b) 18 (c) 289 (d) 23
  2. 2.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  3. 3.What is the distance between the points (7, 17) and (13, 9)? (a) 14 (b) 11 (c) 100 (d) 10
  4. 4.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  5. 5.What is the distance between the points (3, 0) and (9, 8)? (a) 100 (b) 11 (c) 14 (d) 10
  6. 6.What is the midpoint of the line joining (1, 13) and (9, 5)? (a) (9, 5) (b) (4, 4) (c) (5, 9) (d) (10, 18)
  7. 7.What is the midpoint of the line joining (2, 7) and (6, 3)? (a) (5, 4) (b) (4, 5) (c) (2, 2) (d) (8, 10)
  8. 8.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  9. 9.What is the midpoint of the line joining (3, 7) and (7, 17)? (a) (10, 24) (b) (5, 12) (c) (2, 5) (d) (12, 5)
  10. 10.What is the midpoint of the line joining (2, 15) and (4, 7)? (a) (11, 3) (b) (6, 22) (c) (1, 4) (d) (3, 11)
  11. 11.What is the distance between the points (3, 8) and (6, 12)? (a) 6 (b) 5 (c) 7 (d) 25
  12. 12.In which quadrant does the point (7, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  13. 13.What is the distance between the points (3, 18) and (15, 2)? (a) 20 (b) 400 (c) 21 (d) 28
  14. 14.What is the midpoint of the line joining (0, 6) and (10, 10)? (a) (5, 2) (b) (8, 5) (c) (10, 16) (d) (5, 8)
  15. 15.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  16. 16.What is the midpoint of the line joining (0, 7) and (4, 17)? (a) (12, 2) (b) (2, 5) (c) (4, 24) (d) (2, 12)
  17. 17.What is the distance between the points (3, 21) and (12, 9)? (a) 15 (b) 225 (c) 21 (d) 16
  18. 18.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  19. 19.What is the distance between the points (2, 0) and (17, 8)? (a) 17 (b) 289 (c) 23 (d) 18
  20. 20.What is the distance between the points (7, 10) and (11, 7)? (a) 5 (b) 6 (c) 25 (d) 7
  21. 21.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
  22. 22.What is the midpoint of the line joining (5, 7) and (9, 1)? (a) (14, 8) (b) (2, 3) (c) (4, 7) (d) (7, 4)
  23. 23.What is the distance between the points (5, 2) and (13, 17)? (a) 17 (b) 23 (c) 18 (d) 289
  24. 24.What is the distance between the points (1, 7) and (6, 19)? (a) 17 (b) 13 (c) 14 (d) 169
  25. 25.In which quadrant does the point (4, −7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  26. 26.In which quadrant does the point (4, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  27. 27.In which quadrant does the point (−5, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  28. 28.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
  29. 29.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
  30. 30.What is the distance between the points (4, 4) and (7, 8)? (a) 7 (b) 5 (c) 6 (d) 25
  31. 31.In which quadrant does the point (−1, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  32. 32.In which quadrant does the point (−7, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  33. 33.In which quadrant does the point (−8, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  34. 34.In which quadrant does the point (2, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  35. 35.What is the midpoint of the line joining (6, 15) and (16, 5)? (a) (11, 10) (b) (5, 5) (c) (22, 20) (d) (10, 11)
  36. 36.In which quadrant does the point (−9, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  37. 37.What is the distance between the points (2, 12) and (11, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  38. 38.What is the distance between the points (1, 5) and (5, 2)? (a) 7 (b) 6 (c) 5 (d) 25
  39. 39.In which quadrant does the point (−4, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.In which quadrant does the point (6, −8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant

Answer key

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

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