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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 868 · 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 (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 16 (d) 225
  2. 2.What is the distance between the points (8, 13) and (20, 8)? (a) 169 (b) 13 (c) 14 (d) 17
  3. 3.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
  4. 4.What is the distance between the points (0, 4) and (7, 28)? (a) 25 (b) 31 (c) 625 (d) 26
  5. 5.In which quadrant does the point (−4, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  6. 6.What is the midpoint of the line joining (6, 9) and (10, 1)? (a) (16, 10) (b) (8, 5) (c) (5, 8) (d) (2, 4)
  7. 7.In which quadrant does the point (−1, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  8. 8.What is the midpoint of the line joining (0, 9) and (10, 3)? (a) (6, 5) (b) (10, 12) (c) (5, 3) (d) (5, 6)
  9. 9.What is the midpoint of the line joining (10, 12) and (14, 0)? (a) (24, 12) (b) (6, 12) (c) (12, 6) (d) (2, 6)
  10. 10.What is the midpoint of the line joining (9, 13) and (11, 7)? (a) (20, 20) (b) (10, 10) (c) (11, 10) (d) (1, 3)
  11. 11.What is the midpoint of the line joining (5, 10) and (17, 2)? (a) (6, 4) (b) (6, 11) (c) (11, 6) (d) (22, 12)
  12. 12.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  13. 13.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
  14. 14.What is the midpoint of the line joining (2, 20) and (10, 10)? (a) (12, 30) (b) (15, 6) (c) (6, 15) (d) (4, 5)
  15. 15.What is the distance between the points (4, 11) and (12, 5)? (a) 11 (b) 10 (c) 100 (d) 14
  16. 16.What is the midpoint of the line joining (1, 15) and (7, 5)? (a) (3, 5) (b) (10, 4) (c) (4, 10) (d) (8, 20)
  17. 17.In which quadrant does the point (−5, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  18. 18.What is the distance between the points (1, 14) and (13, 9)? (a) 13 (b) 169 (c) 17 (d) 14
  19. 19.In which quadrant does the point (4, 6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  20. 20.What is the distance between the points (4, 4) and (8, 1)? (a) 7 (b) 6 (c) 5 (d) 25
  21. 21.What is the distance between the points (5, 9) and (11, 1)? (a) 11 (b) 10 (c) 100 (d) 14
  22. 22.In which quadrant does the point (−7, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  23. 23.What is the midpoint of the line joining (10, 0) and (20, 12)? (a) (30, 12) (b) (5, 6) (c) (15, 6) (d) (6, 15)
  24. 24.What is the distance between the points (1, 9) and (6, 21)? (a) 169 (b) 14 (c) 17 (d) 13
  25. 25.In which quadrant does the point (1, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  26. 26.What is the midpoint of the line joining (2, 3) and (10, 15)? (a) (6, 9) (b) (12, 18) (c) (4, 6) (d) (9, 6)
  27. 27.In which quadrant does the point (1, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  28. 28.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  29. 29.What is the distance between the points (0, 4) and (8, 19)? (a) 17 (b) 289 (c) 18 (d) 23
  30. 30.What is the distance between the points (9, 2) and (17, 17)? (a) 23 (b) 289 (c) 18 (d) 17
  31. 31.What is the midpoint of the line joining (7, 0) and (11, 6)? (a) (18, 6) (b) (3, 9) (c) (2, 3) (d) (9, 3)
  32. 32.In which quadrant does the point (6, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  33. 33.What is the midpoint of the line joining (3, 11) and (9, 1)? (a) (6, 6) (b) (7, 6) (c) (3, 5) (d) (12, 12)
  34. 34.What is the distance between the points (2, 1) and (11, 13)? (a) 15 (b) 225 (c) 21 (d) 16
  35. 35.What is the midpoint of the line joining (5, 9) and (9, 13)? (a) (11, 7) (b) (7, 11) (c) (14, 22) (d) (2, 2)
  36. 36.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  37. 37.In which quadrant does the point (1, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  38. 38.In which quadrant does the point (−3, −4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  39. 39.In which quadrant does the point (−3, 6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  40. 40.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169

Answer key

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

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