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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 320 · 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 (5, 2) and (14, 14)? (a) 225 (b) 16 (c) 15 (d) 21
  2. 2.What is the distance between the points (9, 1) and (33, 8)? (a) 26 (b) 31 (c) 625 (d) 25
  3. 3.In which quadrant does the point (−3, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  4. 4.What is the midpoint of the line joining (3, 8) and (9, 18)? (a) (3, 5) (b) (12, 26) (c) (13, 6) (d) (6, 13)
  5. 5.What is the midpoint of the line joining (0, 15) and (8, 9)? (a) (12, 4) (b) (8, 24) (c) (4, 12) (d) (4, 3)
  6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  7. 7.What is the distance between the points (2, 4) and (6, 7)? (a) 6 (b) 5 (c) 7 (d) 25
  8. 8.What is the midpoint of the line joining (9, 16) and (13, 4)? (a) (22, 20) (b) (2, 6) (c) (10, 11) (d) (11, 10)
  9. 9.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  10. 10.In which quadrant does the point (6, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  11. 11.In which quadrant does the point (6, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  12. 12.What is the midpoint of the line joining (0, 15) and (12, 3)? (a) (6, 6) (b) (6, 9) (c) (9, 6) (d) (12, 18)
  13. 13.What is the distance between the points (1, 1) and (8, 25)? (a) 625 (b) 31 (c) 26 (d) 25
  14. 14.What is the midpoint of the line joining (1, 0) and (13, 2)? (a) (1, 7) (b) (14, 2) (c) (6, 1) (d) (7, 1)
  15. 15.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  16. 16.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  17. 17.What is the midpoint of the line joining (1, 5) and (5, 1)? (a) (2, 2) (b) (3, 3) (c) (4, 3) (d) (6, 6)
  18. 18.What is the distance between the points (2, 33) and (9, 9)? (a) 25 (b) 26 (c) 31 (d) 625
  19. 19.What is the distance between the points (0, 0) and (12, 16)? (a) 20 (b) 28 (c) 400 (d) 21
  20. 20.What is the midpoint of the line joining (9, 0) and (19, 12)? (a) (14, 6) (b) (5, 6) (c) (28, 12) (d) (6, 14)
  21. 21.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  22. 22.What is the distance between the points (0, 4) and (6, 12)? (a) 11 (b) 14 (c) 10 (d) 100
  23. 23.What is the midpoint of the line joining (8, 0) and (16, 10)? (a) (24, 10) (b) (12, 5) (c) (5, 12) (d) (4, 5)
  24. 24.What is the distance between the points (8, 2) and (11, 6)? (a) 25 (b) 6 (c) 5 (d) 7
  25. 25.What is the distance between the points (0, 1) and (24, 8)? (a) 625 (b) 26 (c) 31 (d) 25
  26. 26.What is the distance between the points (8, 3) and (32, 10)? (a) 31 (b) 625 (c) 26 (d) 25
  27. 27.What is the distance between the points (1, 0) and (5, 3)? (a) 7 (b) 25 (c) 6 (d) 5
  28. 28.What is the distance between the points (4, 5) and (13, 17)? (a) 225 (b) 16 (c) 21 (d) 15
  29. 29.In which quadrant does the point (−9, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  30. 30.In which quadrant does the point (8, 6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  31. 31.In which quadrant does the point (7, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  32. 32.In which quadrant does the point (1, −7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  33. 33.In which quadrant does the point (−1, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  34. 34.What is the midpoint of the line joining (2, 7) and (4, 1)? (a) (4, 3) (b) (1, 3) (c) (6, 8) (d) (3, 4)
  35. 35.What is the midpoint of the line joining (2, 9) and (6, 17)? (a) (4, 13) (b) (13, 4) (c) (8, 26) (d) (2, 4)
  36. 36.What is the distance between the points (8, 15) and (13, 3)? (a) 169 (b) 14 (c) 17 (d) 13
  37. 37.What is the distance between the points (0, 2) and (8, 17)? (a) 18 (b) 17 (c) 289 (d) 23
  38. 38.What is the distance between the points (2, 4) and (9, 28)? (a) 625 (b) 31 (c) 25 (d) 26
  39. 39.What is the midpoint of the line joining (4, 9) and (16, 13)? (a) (20, 22) (b) (6, 2) (c) (11, 10) (d) (10, 11)
  40. 40.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289

Answer key

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

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