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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 440 · 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 (9, 15) and (13, 9)? (a) (12, 11) (b) (22, 24) (c) (11, 12) (d) (2, 3)
  2. 2.What is the midpoint of the line joining (0, 5) and (6, 1)? (a) (4, 3) (b) (3, 3) (c) (6, 6) (d) (3, 2)
  3. 3.In which quadrant does the point (1, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  4. 4.What is the midpoint of the line joining (3, 3) and (7, 1)? (a) (2, 1) (b) (5, 2) (c) (10, 4) (d) (2, 5)
  5. 5.What is the distance between the points (0, 8) and (4, 5)? (a) 6 (b) 25 (c) 5 (d) 7
  6. 6.In which quadrant does the point (3, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  7. 7.What is the distance between the points (4, 16) and (9, 4)? (a) 13 (b) 17 (c) 14 (d) 169
  8. 8.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  9. 9.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  10. 10.What is the midpoint of the line joining (6, 0) and (18, 8)? (a) (12, 4) (b) (4, 12) (c) (6, 4) (d) (24, 8)
  11. 11.What is the midpoint of the line joining (2, 4) and (8, 16)? (a) (3, 6) (b) (10, 5) (c) (5, 10) (d) (10, 20)
  12. 12.In which quadrant does the point (−9, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  13. 13.What is the midpoint of the line joining (1, 0) and (7, 4)? (a) (8, 4) (b) (2, 4) (c) (4, 2) (d) (3, 2)
  14. 14.What is the distance between the points (1, 9) and (13, 18)? (a) 21 (b) 15 (c) 225 (d) 16
  15. 15.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  16. 16.In which quadrant does the point (4, −2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  17. 17.What is the distance between the points (2, 13) and (11, 1)? (a) 15 (b) 16 (c) 21 (d) 225
  18. 18.In which quadrant does the point (−7, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  19. 19.In which quadrant does the point (7, −6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  20. 20.In which quadrant does the point (−4, −2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  21. 21.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  22. 22.In which quadrant does the point (2, 9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  23. 23.What is the distance between the points (1, 5) and (16, 13)? (a) 18 (b) 17 (c) 23 (d) 289
  24. 24.In which quadrant does the point (6, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  25. 25.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  26. 26.What is the distance between the points (6, 8) and (14, 23)? (a) 23 (b) 17 (c) 18 (d) 289
  27. 27.In which quadrant does the point (9, 8) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  28. 28.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  29. 29.What is the distance between the points (2, 17) and (8, 9)? (a) 100 (b) 10 (c) 14 (d) 11
  30. 30.In which quadrant does the point (−8, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  31. 31.What is the distance between the points (1, 19) and (13, 3)? (a) 21 (b) 28 (c) 20 (d) 400
  32. 32.In which quadrant does the point (3, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  33. 33.What is the midpoint of the line joining (6, 0) and (14, 4)? (a) (4, 2) (b) (10, 2) (c) (2, 10) (d) (20, 4)
  34. 34.What is the distance between the points (5, 8) and (12, 32)? (a) 31 (b) 625 (c) 26 (d) 25
  35. 35.What is the midpoint of the line joining (0, 13) and (2, 5)? (a) (1, 9) (b) (1, 4) (c) (9, 1) (d) (2, 18)
  36. 36.What is the distance between the points (8, 5) and (20, 21)? (a) 21 (b) 400 (c) 20 (d) 28
  37. 37.What is the distance between the points (0, 6) and (12, 15)? (a) 15 (b) 16 (c) 225 (d) 21
  38. 38.In which quadrant does the point (−5, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  39. 39.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  40. 40.What is the distance between the points (6, 4) and (14, 10)? (a) 100 (b) 14 (c) 11 (d) 10

Answer key

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

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