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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 576 · 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, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  2. 2.What is the midpoint of the line joining (3, 10) and (9, 4)? (a) (12, 14) (b) (3, 3) (c) (7, 6) (d) (6, 7)
  3. 3.What is the distance between the points (5, 2) and (29, 9)? (a) 26 (b) 31 (c) 25 (d) 625
  4. 4.In which quadrant does the point (−2, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  5. 5.What is the midpoint of the line joining (8, 7) and (18, 5)? (a) (5, 1) (b) (13, 6) (c) (6, 13) (d) (26, 12)
  6. 6.In which quadrant does the point (7, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  7. 7.In which quadrant does the point (1, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  8. 8.What is the midpoint of the line joining (8, 7) and (16, 13)? (a) (10, 12) (b) (12, 10) (c) (4, 3) (d) (24, 20)
  9. 9.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
  10. 10.What is the midpoint of the line joining (4, 14) and (12, 8)? (a) (4, 3) (b) (11, 8) (c) (16, 22) (d) (8, 11)
  11. 11.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  12. 12.What is the distance between the points (4, 12) and (9, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  13. 13.What is the distance between the points (2, 4) and (9, 28)? (a) 625 (b) 31 (c) 25 (d) 26
  14. 14.In which quadrant does the point (−4, −1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  15. 15.What is the distance between the points (9, 7) and (13, 10)? (a) 5 (b) 6 (c) 25 (d) 7
  16. 16.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  17. 17.What is the distance between the points (0, 9) and (5, 21)? (a) 13 (b) 17 (c) 169 (d) 14
  18. 18.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  19. 19.What is the midpoint of the line joining (10, 1) and (12, 7)? (a) (1, 3) (b) (22, 8) (c) (4, 11) (d) (11, 4)
  20. 20.What is the distance between the points (5, 23) and (13, 8)? (a) 23 (b) 18 (c) 17 (d) 289
  21. 21.What is the distance between the points (0, 7) and (4, 10)? (a) 5 (b) 7 (c) 25 (d) 6
  22. 22.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  23. 23.In which quadrant does the point (−4, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  24. 24.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  25. 25.What is the distance between the points (7, 1) and (22, 9)? (a) 18 (b) 23 (c) 289 (d) 17
  26. 26.What is the midpoint of the line joining (1, 7) and (11, 3)? (a) (5, 6) (b) (5, 2) (c) (12, 10) (d) (6, 5)
  27. 27.What is the distance between the points (9, 4) and (12, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  28. 28.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  29. 29.In which quadrant does the point (8, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  30. 30.What is the midpoint of the line joining (1, 1) and (13, 5)? (a) (14, 6) (b) (7, 3) (c) (3, 7) (d) (6, 2)
  31. 31.In which quadrant does the point (−6, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  32. 32.What is the distance between the points (9, 2) and (17, 17)? (a) 17 (b) 18 (c) 23 (d) 289
  33. 33.What is the distance between the points (4, 8) and (20, 20)? (a) 21 (b) 28 (c) 400 (d) 20
  34. 34.What is the midpoint of the line joining (0, 6) and (10, 8)? (a) (5, 1) (b) (5, 7) (c) (10, 14) (d) (7, 5)
  35. 35.In which quadrant does the point (6, −7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  36. 36.What is the distance between the points (4, 1) and (16, 10)? (a) 225 (b) 16 (c) 21 (d) 15
  37. 37.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
  38. 38.In which quadrant does the point (6, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  39. 39.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  40. 40.In which quadrant does the point (−7, −4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant

Answer key

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

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