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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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