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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 375 · 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 midpoint of the line joining (3, 9) and (5, 15)? (a) (8, 24) (b) (4, 12) (c) (12, 4) (d) (1, 3)
  2. 2.What is the midpoint of the line joining (9, 9) and (13, 13)? (a) (22, 22) (b) (2, 2) (c) (12, 11) (d) (11, 11)
  3. 3.In which quadrant does the point (7, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  4. 4.What is the midpoint of the line joining (8, 8) and (14, 10)? (a) (9, 11) (b) (11, 9) (c) (3, 1) (d) (22, 18)
  5. 5.In which quadrant does the point (−5, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  6. 6.In which quadrant does the point (−6, 6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  7. 7.What is the midpoint of the line joining (1, 9) and (13, 11)? (a) (6, 1) (b) (7, 10) (c) (10, 7) (d) (14, 20)
  8. 8.What is the distance between the points (0, 1) and (3, 5)? (a) 25 (b) 5 (c) 7 (d) 6
  9. 9.What is the distance between the points (7, 8) and (15, 14)? (a) 10 (b) 14 (c) 100 (d) 11
  10. 10.What is the midpoint of the line joining (4, 3) and (6, 13)? (a) (5, 8) (b) (10, 16) (c) (1, 5) (d) (8, 5)
  11. 11.In which quadrant does the point (−1, 1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  12. 12.What is the distance between the points (8, 11) and (11, 7)? (a) 25 (b) 5 (c) 7 (d) 6
  13. 13.What is the midpoint of the line joining (2, 4) and (8, 16)? (a) (10, 5) (b) (5, 10) (c) (3, 6) (d) (10, 20)
  14. 14.What is the midpoint of the line joining (10, 13) and (22, 1)? (a) (32, 14) (b) (16, 7) (c) (6, 6) (d) (7, 16)
  15. 15.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
  16. 16.What is the midpoint of the line joining (4, 8) and (16, 12)? (a) (6, 2) (b) (10, 10) (c) (11, 10) (d) (20, 20)
  17. 17.What is the midpoint of the line joining (5, 20) and (17, 10)? (a) (22, 30) (b) (15, 11) (c) (6, 5) (d) (11, 15)
  18. 18.What is the distance between the points (1, 3) and (7, 11)? (a) 10 (b) 14 (c) 100 (d) 11
  19. 19.In which quadrant does the point (−1, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  20. 20.In which quadrant does the point (9, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  21. 21.In which quadrant does the point (6, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  22. 22.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  23. 23.What is the distance between the points (5, 0) and (14, 12)? (a) 225 (b) 16 (c) 15 (d) 21
  24. 24.In which quadrant does the point (−4, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  25. 25.What is the midpoint of the line joining (7, 6) and (11, 2)? (a) (4, 9) (b) (2, 2) (c) (18, 8) (d) (9, 4)
  26. 26.What is the midpoint of the line joining (3, 1) and (11, 9)? (a) (5, 7) (b) (4, 4) (c) (14, 10) (d) (7, 5)
  27. 27.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  28. 28.In which quadrant does the point (6, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  29. 29.What is the midpoint of the line joining (7, 1) and (9, 13)? (a) (7, 8) (b) (1, 6) (c) (8, 7) (d) (16, 14)
  30. 30.What is the distance between the points (7, 5) and (23, 17)? (a) 20 (b) 28 (c) 400 (d) 21
  31. 31.What is the midpoint of the line joining (0, 3) and (8, 11)? (a) (4, 4) (b) (8, 14) (c) (4, 7) (d) (7, 4)
  32. 32.What is the midpoint of the line joining (1, 3) and (11, 11)? (a) (12, 14) (b) (5, 4) (c) (7, 6) (d) (6, 7)
  33. 33.What is the distance between the points (5, 1) and (11, 9)? (a) 11 (b) 100 (c) 10 (d) 14
  34. 34.In which quadrant does the point (−3, 5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  35. 35.What is the midpoint of the line joining (0, 16) and (10, 8)? (a) (10, 24) (b) (5, 4) (c) (12, 5) (d) (5, 12)
  36. 36.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 21 (d) 28
  37. 37.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  38. 38.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 23 (d) 17
  39. 39.What is the midpoint of the line joining (0, 5) and (6, 15)? (a) (10, 3) (b) (6, 20) (c) (3, 5) (d) (3, 10)
  40. 40.In which quadrant does the point (4, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant

Answer key

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

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