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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 902 · 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 (0, 18) and (12, 9)? (a) 15 (b) 21 (c) 16 (d) 225
  2. 2.What is the midpoint of the line joining (7, 8) and (17, 0)? (a) (12, 4) (b) (4, 12) (c) (24, 8) (d) (5, 4)
  3. 3.What is the midpoint of the line joining (5, 3) and (13, 1)? (a) (2, 9) (b) (9, 2) (c) (18, 4) (d) (4, 1)
  4. 4.What is the distance between the points (8, 31) and (15, 7)? (a) 31 (b) 625 (c) 25 (d) 26
  5. 5.What is the midpoint of the line joining (5, 9) and (15, 5)? (a) (10, 7) (b) (20, 14) (c) (5, 2) (d) (7, 10)
  6. 6.In which quadrant does the point (2, −9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  7. 7.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  8. 8.In which quadrant does the point (−9, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  9. 9.What is the distance between the points (9, 10) and (24, 2)? (a) 18 (b) 17 (c) 289 (d) 23
  10. 10.What is the distance between the points (8, 0) and (17, 12)? (a) 21 (b) 225 (c) 16 (d) 15
  11. 11.What is the midpoint of the line joining (7, 7) and (9, 11)? (a) (1, 2) (b) (8, 9) (c) (16, 18) (d) (9, 8)
  12. 12.In which quadrant does the point (−6, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  13. 13.In which quadrant does the point (−2, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  14. 14.What is the midpoint of the line joining (7, 14) and (9, 4)? (a) (9, 8) (b) (16, 18) (c) (8, 9) (d) (1, 5)
  15. 15.In which quadrant does the point (2, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  16. 16.What is the midpoint of the line joining (4, 9) and (14, 17)? (a) (13, 9) (b) (9, 13) (c) (5, 4) (d) (18, 26)
  17. 17.What is the midpoint of the line joining (4, 13) and (10, 1)? (a) (14, 14) (b) (8, 7) (c) (3, 6) (d) (7, 7)
  18. 18.What is the distance between the points (2, 5) and (5, 1)? (a) 5 (b) 25 (c) 7 (d) 6
  19. 19.What is the distance between the points (5, 11) and (29, 4)? (a) 625 (b) 31 (c) 26 (d) 25
  20. 20.In which quadrant does the point (−6, −1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  21. 21.In which quadrant does the point (8, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  22. 22.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
  23. 23.What is the midpoint of the line joining (0, 3) and (4, 11)? (a) (4, 14) (b) (7, 2) (c) (2, 7) (d) (2, 4)
  24. 24.In which quadrant does the point (9, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  25. 25.What is the midpoint of the line joining (9, 10) and (13, 12)? (a) (2, 1) (b) (11, 11) (c) (22, 22) (d) (12, 11)
  26. 26.What is the midpoint of the line joining (5, 16) and (15, 6)? (a) (11, 10) (b) (20, 22) (c) (5, 5) (d) (10, 11)
  27. 27.In which quadrant does the point (3, −7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  28. 28.What is the distance between the points (1, 7) and (4, 3)? (a) 6 (b) 7 (c) 5 (d) 25
  29. 29.What is the midpoint of the line joining (3, 1) and (7, 11)? (a) (10, 12) (b) (6, 5) (c) (5, 6) (d) (2, 5)
  30. 30.In which quadrant does the point (1, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  31. 31.In which quadrant does the point (−9, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  32. 32.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
  33. 33.What is the distance between the points (3, 15) and (11, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  34. 34.In which quadrant does the point (7, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  35. 35.What is the distance between the points (3, 12) and (9, 4)? (a) 14 (b) 11 (c) 10 (d) 100
  36. 36.What is the midpoint of the line joining (10, 4) and (22, 12)? (a) (8, 16) (b) (16, 8) (c) (32, 16) (d) (6, 4)
  37. 37.In which quadrant does the point (−5, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  38. 38.What is the midpoint of the line joining (5, 1) and (9, 7)? (a) (2, 3) (b) (7, 4) (c) (14, 8) (d) (4, 7)
  39. 39.In which quadrant does the point (6, 6) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10

Answer key

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

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