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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 731 · 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 (9, 8) and (12, 4)? (a) 5 (b) 7 (c) 6 (d) 25
  2. 2.In which quadrant does the point (−1, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  3. 3.What is the distance between the points (4, 18) and (16, 2)? (a) 20 (b) 21 (c) 28 (d) 400
  4. 4.What is the distance between the points (4, 14) and (19, 6)? (a) 17 (b) 18 (c) 289 (d) 23
  5. 5.In which quadrant does the point (3, −8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  7. 7.What is the distance between the points (0, 5) and (7, 29)? (a) 625 (b) 31 (c) 26 (d) 25
  8. 8.What is the midpoint of the line joining (7, 8) and (19, 10)? (a) (9, 13) (b) (26, 18) (c) (13, 9) (d) (6, 1)
  9. 9.What is the distance between the points (0, 0) and (8, 6)? (a) 14 (b) 100 (c) 10 (d) 11
  10. 10.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  11. 11.What is the distance between the points (6, 9) and (14, 15)? (a) 11 (b) 14 (c) 10 (d) 100
  12. 12.In which quadrant does the point (−1, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  13. 13.What is the distance between the points (0, 15) and (8, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  14. 14.In which quadrant does the point (−2, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  15. 15.In which quadrant does the point (8, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  16. 16.What is the distance between the points (2, 15) and (10, 0)? (a) 17 (b) 23 (c) 18 (d) 289
  17. 17.What is the midpoint of the line joining (10, 12) and (12, 2)? (a) (1, 5) (b) (7, 11) (c) (22, 14) (d) (11, 7)
  18. 18.In which quadrant does the point (5, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  19. 19.What is the distance between the points (8, 5) and (11, 9)? (a) 6 (b) 25 (c) 7 (d) 5
  20. 20.In which quadrant does the point (6, −6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  21. 21.In which quadrant does the point (4, −3) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  22. 22.What is the midpoint of the line joining (2, 1) and (10, 9)? (a) (4, 4) (b) (5, 6) (c) (12, 10) (d) (6, 5)
  23. 23.What is the midpoint of the line joining (9, 8) and (11, 16)? (a) (12, 10) (b) (20, 24) (c) (1, 4) (d) (10, 12)
  24. 24.What is the distance between the points (0, 8) and (16, 20)? (a) 20 (b) 28 (c) 21 (d) 400
  25. 25.In which quadrant does the point (6, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  26. 26.What is the distance between the points (8, 10) and (32, 3)? (a) 31 (b) 625 (c) 25 (d) 26
  27. 27.In which quadrant does the point (3, 1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  28. 28.What is the distance between the points (3, 1) and (27, 8)? (a) 26 (b) 31 (c) 625 (d) 25
  29. 29.In which quadrant does the point (9, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  30. 30.What is the midpoint of the line joining (2, 4) and (4, 12)? (a) (3, 8) (b) (6, 16) (c) (1, 4) (d) (8, 3)
  31. 31.In which quadrant does the point (−9, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  32. 32.What is the distance between the points (0, 11) and (6, 3)? (a) 11 (b) 100 (c) 10 (d) 14
  33. 33.In which quadrant does the point (4, 6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  34. 34.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  35. 35.In which quadrant does the point (−6, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  36. 36.What is the midpoint of the line joining (3, 7) and (13, 19)? (a) (8, 13) (b) (16, 26) (c) (5, 6) (d) (13, 8)
  37. 37.What is the midpoint of the line joining (8, 2) and (18, 10)? (a) (6, 13) (b) (26, 12) (c) (13, 6) (d) (5, 4)
  38. 38.What is the midpoint of the line joining (10, 6) and (20, 8)? (a) (15, 7) (b) (5, 1) (c) (30, 14) (d) (7, 15)
  39. 39.In which quadrant does the point (5, 5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  40. 40.In which quadrant does the point (7, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant

Answer key

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

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