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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 394 · 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 (3, 15) and (11, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  2. 2.What is the distance between the points (3, 3) and (27, 10)? (a) 31 (b) 25 (c) 625 (d) 26
  3. 3.What is the distance between the points (0, 2) and (6, 10)? (a) 11 (b) 100 (c) 10 (d) 14
  4. 4.What is the distance between the points (2, 0) and (18, 12)? (a) 28 (b) 21 (c) 400 (d) 20
  5. 5.In which quadrant does the point (−1, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  6. 6.What is the distance between the points (4, 7) and (12, 1)? (a) 100 (b) 10 (c) 11 (d) 14
  7. 7.What is the midpoint of the line joining (3, 10) and (7, 0)? (a) (10, 10) (b) (6, 5) (c) (2, 5) (d) (5, 5)
  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 (12, 5) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  10. 10.In which quadrant does the point (−1, −7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  11. 11.In which quadrant does the point (5, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  12. 12.What is the distance between the points (0, 21) and (9, 9)? (a) 21 (b) 16 (c) 225 (d) 15
  13. 13.What is the distance between the points (0, 27) and (7, 3)? (a) 625 (b) 26 (c) 25 (d) 31
  14. 14.What is the midpoint of the line joining (0, 10) and (6, 16)? (a) (6, 26) (b) (3, 13) (c) (3, 3) (d) (13, 3)
  15. 15.What is the distance between the points (2, 12) and (11, 0)? (a) 15 (b) 16 (c) 21 (d) 225
  16. 16.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  17. 17.What is the distance between the points (0, 25) and (12, 9)? (a) 20 (b) 21 (c) 28 (d) 400
  18. 18.What is the distance between the points (7, 29) and (14, 5)? (a) 625 (b) 31 (c) 26 (d) 25
  19. 19.In which quadrant does the point (−3, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  20. 20.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 225 (c) 16 (d) 15
  21. 21.In which quadrant does the point (6, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  22. 22.What is the midpoint of the line joining (9, 1) and (11, 9)? (a) (1, 4) (b) (10, 5) (c) (5, 10) (d) (20, 10)
  23. 23.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  24. 24.What is the midpoint of the line joining (3, 16) and (11, 10)? (a) (4, 3) (b) (14, 26) (c) (13, 7) (d) (7, 13)
  25. 25.What is the distance between the points (2, 0) and (14, 9)? (a) 16 (b) 21 (c) 225 (d) 15
  26. 26.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  27. 27.In which quadrant does the point (−7, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  28. 28.In which quadrant does the point (−8, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  29. 29.In which quadrant does the point (−4, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  30. 30.What is the midpoint of the line joining (7, 14) and (9, 10)? (a) (8, 12) (b) (1, 2) (c) (16, 24) (d) (12, 8)
  31. 31.In which quadrant does the point (−9, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  32. 32.What is the distance between the points (7, 3) and (11, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  33. 33.What is the distance between the points (7, 14) and (12, 2)? (a) 13 (b) 14 (c) 169 (d) 17
  34. 34.In which quadrant does the point (−5, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  35. 35.What is the midpoint of the line joining (1, 10) and (7, 2)? (a) (4, 6) (b) (3, 4) (c) (6, 4) (d) (8, 12)
  36. 36.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  37. 37.What is the midpoint of the line joining (1, 2) and (13, 4)? (a) (6, 1) (b) (3, 7) (c) (7, 3) (d) (14, 6)
  38. 38.What is the distance between the points (8, 0) and (20, 9)? (a) 21 (b) 15 (c) 225 (d) 16
  39. 39.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  40. 40.In which quadrant does the point (9, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant

Answer key

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

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