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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 261 · 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 (1, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  2. 2.What is the midpoint of the line joining (8, 10) and (10, 4)? (a) (9, 7) (b) (7, 9) (c) (18, 14) (d) (1, 3)
  3. 3.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  4. 4.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  5. 5.What is the distance between the points (4, 8) and (16, 3)? (a) 14 (b) 13 (c) 17 (d) 169
  6. 6.What is the midpoint of the line joining (7, 15) and (15, 5)? (a) (10, 11) (b) (11, 10) (c) (22, 20) (d) (4, 5)
  7. 7.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  8. 8.What is the midpoint of the line joining (10, 0) and (22, 4)? (a) (32, 4) (b) (6, 2) (c) (16, 2) (d) (2, 16)
  9. 9.What is the distance between the points (1, 19) and (6, 7)? (a) 14 (b) 17 (c) 169 (d) 13
  10. 10.What is the distance between the points (0, 0) and (6, 8)? (a) 10 (b) 14 (c) 11 (d) 100
  11. 11.What is the distance between the points (0, 20) and (9, 8)? (a) 225 (b) 21 (c) 15 (d) 16
  12. 12.What is the midpoint of the line joining (7, 4) and (17, 2)? (a) (3, 12) (b) (5, 1) (c) (24, 6) (d) (12, 3)
  13. 13.In which quadrant does the point (−4, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  14. 14.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 625 (c) 26 (d) 31
  15. 15.What is the distance between the points (4, 7) and (8, 10)? (a) 25 (b) 5 (c) 7 (d) 6
  16. 16.In which quadrant does the point (9, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  17. 17.In which quadrant does the point (−9, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  18. 18.What is the distance between the points (8, 4) and (15, 28)? (a) 26 (b) 625 (c) 31 (d) 25
  19. 19.In which quadrant does the point (−9, 5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  20. 20.What is the distance between the points (5, 7) and (17, 2)? (a) 13 (b) 169 (c) 17 (d) 14
  21. 21.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  22. 22.What is the distance between the points (1, 5) and (8, 29)? (a) 625 (b) 26 (c) 25 (d) 31
  23. 23.What is the midpoint of the line joining (2, 11) and (10, 3)? (a) (6, 7) (b) (4, 4) (c) (7, 6) (d) (12, 14)
  24. 24.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  25. 25.What is the distance between the points (1, 16) and (10, 4)? (a) 15 (b) 16 (c) 21 (d) 225
  26. 26.What is the distance between the points (6, 6) and (9, 10)? (a) 6 (b) 25 (c) 7 (d) 5
  27. 27.In which quadrant does the point (−1, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  28. 28.What is the midpoint of the line joining (7, 0) and (17, 6)? (a) (5, 3) (b) (3, 12) (c) (24, 6) (d) (12, 3)
  29. 29.In which quadrant does the point (−8, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  30. 30.What is the midpoint of the line joining (10, 1) and (14, 9)? (a) (5, 12) (b) (2, 4) (c) (24, 10) (d) (12, 5)
  31. 31.What is the midpoint of the line joining (2, 16) and (8, 4)? (a) (3, 6) (b) (5, 10) (c) (10, 20) (d) (10, 5)
  32. 32.What is the midpoint of the line joining (9, 9) and (11, 11)? (a) (1, 1) (b) (11, 10) (c) (20, 20) (d) (10, 10)
  33. 33.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
  34. 34.What is the distance between the points (8, 2) and (14, 10)? (a) 100 (b) 14 (c) 11 (d) 10
  35. 35.What is the midpoint of the line joining (7, 4) and (15, 16)? (a) (11, 10) (b) (4, 6) (c) (22, 20) (d) (10, 11)
  36. 36.In which quadrant does the point (3, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  37. 37.In which quadrant does the point (6, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  38. 38.In which quadrant does the point (2, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  39. 39.In which quadrant does the point (5, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  40. 40.In which quadrant does the point (7, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant

Answer key

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

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