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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 325 · 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 (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
  2. 2.What is the distance between the points (5, 21) and (13, 6)? (a) 18 (b) 289 (c) 23 (d) 17
  3. 3.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
  4. 4.What is the midpoint of the line joining (6, 4) and (8, 8)? (a) (7, 6) (b) (6, 7) (c) (14, 12) (d) (1, 2)
  5. 5.What is the distance between the points (4, 10) and (7, 6)? (a) 6 (b) 5 (c) 25 (d) 7
  6. 6.What is the distance between the points (7, 11) and (19, 2)? (a) 225 (b) 15 (c) 21 (d) 16
  7. 7.What is the distance between the points (9, 20) and (21, 4)? (a) 21 (b) 20 (c) 400 (d) 28
  8. 8.What is the distance between the points (2, 7) and (14, 23)? (a) 21 (b) 28 (c) 20 (d) 400
  9. 9.In which quadrant does the point (−9, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  10. 10.In which quadrant does the point (−9, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  11. 11.What is the midpoint of the line joining (9, 6) and (11, 18)? (a) (20, 24) (b) (12, 10) (c) (1, 6) (d) (10, 12)
  12. 12.In which quadrant does the point (−5, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  13. 13.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  14. 14.In which quadrant does the point (−9, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  15. 15.In which quadrant does the point (1, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  16. 16.What is the distance between the points (3, 2) and (10, 26)? (a) 25 (b) 625 (c) 31 (d) 26
  17. 17.What is the distance between the points (9, 0) and (24, 8)? (a) 17 (b) 23 (c) 289 (d) 18
  18. 18.In which quadrant does the point (4, −7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  19. 19.In which quadrant does the point (1, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  20. 20.What is the midpoint of the line joining (1, 12) and (11, 0)? (a) (7, 6) (b) (5, 6) (c) (12, 12) (d) (6, 6)
  21. 21.What is the distance between the points (8, 1) and (11, 5)? (a) 6 (b) 7 (c) 5 (d) 25
  22. 22.What is the distance between the points (2, 12) and (7, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  23. 23.What is the distance between the points (2, 5) and (14, 10)? (a) 17 (b) 13 (c) 14 (d) 169
  24. 24.What is the distance between the points (1, 20) and (17, 8)? (a) 20 (b) 21 (c) 400 (d) 28
  25. 25.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  26. 26.What is the distance between the points (0, 9) and (12, 25)? (a) 400 (b) 21 (c) 20 (d) 28
  27. 27.What is the midpoint of the line joining (6, 12) and (10, 2)? (a) (16, 14) (b) (2, 5) (c) (8, 7) (d) (7, 8)
  28. 28.What is the distance between the points (0, 3) and (24, 10)? (a) 25 (b) 26 (c) 31 (d) 625
  29. 29.What is the midpoint of the line joining (5, 14) and (17, 6)? (a) (6, 4) (b) (11, 10) (c) (22, 20) (d) (10, 11)
  30. 30.What is the distance between the points (8, 12) and (12, 9)? (a) 7 (b) 6 (c) 25 (d) 5
  31. 31.What is the midpoint of the line joining (0, 3) and (2, 1)? (a) (2, 4) (b) (2, 1) (c) (1, 1) (d) (1, 2)
  32. 32.In which quadrant does the point (−3, −5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  33. 33.What is the midpoint of the line joining (4, 2) and (12, 0)? (a) (4, 1) (b) (16, 2) (c) (1, 8) (d) (8, 1)
  34. 34.What is the midpoint of the line joining (4, 4) and (10, 0)? (a) (3, 2) (b) (2, 7) (c) (7, 2) (d) (14, 4)
  35. 35.What is the distance between the points (0, 1) and (9, 13)? (a) 21 (b) 225 (c) 15 (d) 16
  36. 36.What is the distance between the points (0, 8) and (4, 11)? (a) 25 (b) 6 (c) 7 (d) 5
  37. 37.In which quadrant does the point (−8, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  38. 38.What is the distance between the points (1, 2) and (25, 9)? (a) 25 (b) 26 (c) 625 (d) 31
  39. 39.In which quadrant does the point (−1, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  40. 40.In which quadrant does the point (4, 5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant

Answer key

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

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