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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 738 · 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 midpoint of the line joining (1, 3) and (3, 15)? (a) (9, 2) (b) (2, 9) (c) (4, 18) (d) (1, 6)
  2. 2.What is the distance between the points (1, 17) and (10, 5)? (a) 16 (b) 15 (c) 225 (d) 21
  3. 3.What is the distance between the points (0, 14) and (12, 5)? (a) 21 (b) 225 (c) 15 (d) 16
  4. 4.In which quadrant does the point (3, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  5. 5.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  6. 6.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  7. 7.What is the midpoint of the line joining (5, 8) and (9, 0)? (a) (4, 7) (b) (7, 4) (c) (14, 8) (d) (2, 4)
  8. 8.What is the distance between the points (4, 1) and (11, 25)? (a) 31 (b) 25 (c) 625 (d) 26
  9. 9.What is the distance between the points (6, 25) and (18, 9)? (a) 28 (b) 20 (c) 21 (d) 400
  10. 10.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  11. 11.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 14 (c) 169 (d) 17
  12. 12.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  13. 13.In which quadrant does the point (−7, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  14. 14.What is the distance between the points (1, 2) and (5, 5)? (a) 6 (b) 7 (c) 5 (d) 25
  15. 15.What is the distance between the points (5, 2) and (17, 7)? (a) 169 (b) 14 (c) 17 (d) 13
  16. 16.In which quadrant does the point (2, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  17. 17.What is the distance between the points (2, 9) and (5, 5)? (a) 5 (b) 7 (c) 25 (d) 6
  18. 18.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  19. 19.In which quadrant does the point (−3, 6) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  20. 20.What is the midpoint of the line joining (1, 21) and (9, 9)? (a) (4, 6) (b) (5, 15) (c) (10, 30) (d) (15, 5)
  21. 21.What is the midpoint of the line joining (2, 4) and (4, 6)? (a) (5, 3) (b) (1, 1) (c) (6, 10) (d) (3, 5)
  22. 22.What is the distance between the points (8, 2) and (11, 6)? (a) 6 (b) 5 (c) 25 (d) 7
  23. 23.What is the midpoint of the line joining (5, 8) and (15, 18)? (a) (20, 26) (b) (10, 13) (c) (5, 5) (d) (13, 10)
  24. 24.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  25. 25.What is the midpoint of the line joining (6, 8) and (10, 20)? (a) (8, 14) (b) (14, 8) (c) (16, 28) (d) (2, 6)
  26. 26.What is the midpoint of the line joining (10, 19) and (22, 9)? (a) (6, 5) (b) (32, 28) (c) (14, 16) (d) (16, 14)
  27. 27.What is the distance between the points (0, 15) and (9, 3)? (a) 21 (b) 225 (c) 16 (d) 15
  28. 28.What is the distance between the points (0, 7) and (12, 2)? (a) 17 (b) 169 (c) 14 (d) 13
  29. 29.What is the distance between the points (7, 12) and (22, 4)? (a) 18 (b) 17 (c) 289 (d) 23
  30. 30.In which quadrant does the point (−9, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  31. 31.What is the distance between the points (2, 1) and (14, 10)? (a) 21 (b) 16 (c) 15 (d) 225
  32. 32.In which quadrant does the point (3, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  33. 33.In which quadrant does the point (2, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  34. 34.What is the midpoint of the line joining (2, 8) and (6, 4)? (a) (6, 4) (b) (2, 2) (c) (8, 12) (d) (4, 6)
  35. 35.What is the distance between the points (3, 4) and (6, 8)? (a) 25 (b) 5 (c) 7 (d) 6
  36. 36.In which quadrant does the point (−6, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  37. 37.In which quadrant does the point (7, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  38. 38.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
  39. 39.What is the distance between the points (0, 7) and (3, 3)? (a) 7 (b) 5 (c) 25 (d) 6
  40. 40.In which quadrant does the point (−3, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant

Answer key

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

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