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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 403 · 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, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
  2. 2.What is the midpoint of the line joining (6, 4) and (14, 2)? (a) (4, 1) (b) (20, 6) (c) (10, 3) (d) (3, 10)
  3. 3.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
  4. 4.What is the distance between the points (8, 4) and (12, 7)? (a) 6 (b) 7 (c) 25 (d) 5
  5. 5.In which quadrant does the point (−9, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  6. 6.What is the midpoint of the line joining (6, 10) and (14, 22)? (a) (10, 16) (b) (20, 32) (c) (4, 6) (d) (16, 10)
  7. 7.What is the distance between the points (4, 0) and (7, 4)? (a) 7 (b) 6 (c) 25 (d) 5
  8. 8.What is the distance between the points (2, 7) and (5, 3)? (a) 25 (b) 5 (c) 6 (d) 7
  9. 9.What is the distance between the points (1, 0) and (13, 9)? (a) 21 (b) 225 (c) 16 (d) 15
  10. 10.In which quadrant does the point (6, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  11. 11.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
  12. 12.What is the distance between the points (8, 0) and (23, 8)? (a) 23 (b) 18 (c) 17 (d) 289
  13. 13.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  14. 14.What is the midpoint of the line joining (9, 14) and (11, 6)? (a) (20, 20) (b) (1, 4) (c) (11, 10) (d) (10, 10)
  15. 15.What is the midpoint of the line joining (7, 0) and (19, 8)? (a) (6, 4) (b) (26, 8) (c) (4, 13) (d) (13, 4)
  16. 16.In which quadrant does the point (8, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  17. 17.In which quadrant does the point (−3, −4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  18. 18.What is the midpoint of the line joining (5, 2) and (7, 10)? (a) (12, 12) (b) (1, 4) (c) (6, 6) (d) (7, 6)
  19. 19.In which quadrant does the point (5, 6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  20. 20.What is the midpoint of the line joining (7, 17) and (17, 7)? (a) (12, 12) (b) (13, 12) (c) (24, 24) (d) (5, 5)
  21. 21.What is the distance between the points (4, 19) and (13, 7)? (a) 225 (b) 16 (c) 15 (d) 21
  22. 22.In which quadrant does the point (2, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  23. 23.In which quadrant does the point (4, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  24. 24.What is the distance between the points (3, 5) and (6, 1)? (a) 5 (b) 6 (c) 25 (d) 7
  25. 25.In which quadrant does the point (7, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  26. 26.What is the distance between the points (5, 2) and (13, 17)? (a) 18 (b) 17 (c) 289 (d) 23
  27. 27.In which quadrant does the point (1, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  28. 28.In which quadrant does the point (−1, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  29. 29.In which quadrant does the point (−1, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  30. 30.In which quadrant does the point (−1, 7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  31. 31.What is the midpoint of the line joining (9, 15) and (13, 5)? (a) (10, 11) (b) (22, 20) (c) (2, 5) (d) (11, 10)
  32. 32.In which quadrant does the point (9, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  33. 33.In which quadrant does the point (6, −4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  34. 34.What is the midpoint of the line joining (0, 2) and (10, 0)? (a) (1, 5) (b) (10, 2) (c) (5, 1) (d) (6, 1)
  35. 35.What is the distance between the points (7, 17) and (15, 2)? (a) 18 (b) 289 (c) 17 (d) 23
  36. 36.What is the midpoint of the line joining (6, 2) and (8, 8)? (a) (14, 10) (b) (7, 5) (c) (5, 7) (d) (1, 3)
  37. 37.What is the midpoint of the line joining (9, 1) and (21, 9)? (a) (6, 4) (b) (5, 15) (c) (30, 10) (d) (15, 5)
  38. 38.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  39. 39.In which quadrant does the point (−2, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  40. 40.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100

Answer key

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

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