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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 582 · 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.In which quadrant does the point (8, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  2. 2.What is the distance between the points (3, 4) and (27, 11)? (a) 25 (b) 625 (c) 26 (d) 31
  3. 3.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  4. 4.In which quadrant does the point (6, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  5. 5.What is the distance between the points (3, 8) and (9, 16)? (a) 11 (b) 14 (c) 10 (d) 100
  6. 6.What is the midpoint of the line joining (5, 4) and (9, 0)? (a) (2, 7) (b) (7, 2) (c) (14, 4) (d) (2, 2)
  7. 7.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  8. 8.In which quadrant does the point (6, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  9. 9.What is the distance between the points (5, 1) and (17, 6)? (a) 14 (b) 169 (c) 13 (d) 17
  10. 10.In which quadrant does the point (6, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  11. 11.What is the distance between the points (5, 8) and (9, 11)? (a) 5 (b) 7 (c) 25 (d) 6
  12. 12.In which quadrant does the point (−3, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  13. 13.In which quadrant does the point (8, −9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  14. 14.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  15. 15.In which quadrant does the point (5, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  16. 16.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  17. 17.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
  18. 18.What is the midpoint of the line joining (10, 20) and (16, 10)? (a) (3, 5) (b) (13, 15) (c) (15, 13) (d) (26, 30)
  19. 19.In which quadrant does the point (−8, −2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  20. 20.In which quadrant does the point (−3, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  21. 21.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  22. 22.In which quadrant does the point (−8, −3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  23. 23.What is the distance between the points (5, 16) and (14, 4)? (a) 225 (b) 15 (c) 21 (d) 16
  24. 24.What is the distance between the points (6, 8) and (9, 4)? (a) 6 (b) 7 (c) 25 (d) 5
  25. 25.What is the midpoint of the line joining (3, 1) and (7, 3)? (a) (2, 5) (b) (10, 4) (c) (2, 1) (d) (5, 2)
  26. 26.What is the distance between the points (3, 0) and (15, 9)? (a) 21 (b) 16 (c) 15 (d) 225
  27. 27.What is the distance between the points (6, 7) and (14, 22)? (a) 23 (b) 289 (c) 18 (d) 17
  28. 28.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  29. 29.What is the distance between the points (7, 8) and (15, 23)? (a) 18 (b) 17 (c) 23 (d) 289
  30. 30.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  31. 31.What is the distance between the points (4, 23) and (16, 7)? (a) 21 (b) 20 (c) 28 (d) 400
  32. 32.What is the distance between the points (9, 12) and (15, 4)? (a) 100 (b) 14 (c) 10 (d) 11
  33. 33.What is the distance between the points (3, 19) and (11, 4)? (a) 289 (b) 23 (c) 18 (d) 17
  34. 34.What is the midpoint of the line joining (1, 4) and (13, 14)? (a) (7, 9) (b) (6, 5) (c) (9, 7) (d) (14, 18)
  35. 35.In which quadrant does the point (1, −2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  36. 36.What is the distance between the points (3, 5) and (10, 29)? (a) 25 (b) 31 (c) 26 (d) 625
  37. 37.In which quadrant does the point (−3, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  38. 38.What is the midpoint of the line joining (3, 6) and (15, 2)? (a) (18, 8) (b) (9, 4) (c) (6, 2) (d) (4, 9)
  39. 39.In which quadrant does the point (1, 7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.What is the distance between the points (2, 7) and (11, 19)? (a) 15 (b) 16 (c) 225 (d) 21

Answer key

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

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