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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 761 · 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 (2, 4) and (6, 1)? (a) 25 (b) 6 (c) 5 (d) 7
  2. 2.What is the distance between the points (4, 24) and (11, 0)? (a) 25 (b) 26 (c) 625 (d) 31
  3. 3.What is the distance between the points (1, 21) and (6, 9)? (a) 17 (b) 169 (c) 13 (d) 14
  4. 4.In which quadrant does the point (4, −2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  5. 5.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  6. 6.What is the midpoint of the line joining (1, 17) and (7, 9)? (a) (8, 26) (b) (13, 4) (c) (4, 13) (d) (3, 4)
  7. 7.What is the distance between the points (8, 8) and (12, 5)? (a) 6 (b) 7 (c) 5 (d) 25
  8. 8.In which quadrant does the point (−6, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  9. 9.What is the midpoint of the line joining (1, 14) and (7, 2)? (a) (8, 4) (b) (8, 16) (c) (3, 6) (d) (4, 8)
  10. 10.What is the midpoint of the line joining (2, 5) and (8, 1)? (a) (3, 5) (b) (3, 2) (c) (5, 3) (d) (10, 6)
  11. 11.In which quadrant does the point (3, 8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  12. 12.What is the midpoint of the line joining (2, 15) and (14, 5)? (a) (8, 10) (b) (16, 20) (c) (6, 5) (d) (10, 8)
  13. 13.In which quadrant does the point (3, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  14. 14.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  15. 15.In which quadrant does the point (6, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  16. 16.What is the midpoint of the line joining (1, 4) and (13, 6)? (a) (5, 7) (b) (7, 5) (c) (14, 10) (d) (6, 1)
  17. 17.What is the distance between the points (1, 17) and (13, 1)? (a) 400 (b) 20 (c) 21 (d) 28
  18. 18.What is the distance between the points (2, 14) and (8, 6)? (a) 11 (b) 14 (c) 100 (d) 10
  19. 19.What is the midpoint of the line joining (3, 2) and (9, 6)? (a) (12, 8) (b) (6, 4) (c) (4, 6) (d) (3, 2)
  20. 20.In which quadrant does the point (−3, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  21. 21.In which quadrant does the point (1, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  22. 22.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  23. 23.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  24. 24.What is the midpoint of the line joining (7, 16) and (13, 10)? (a) (13, 10) (b) (20, 26) (c) (3, 3) (d) (10, 13)
  25. 25.In which quadrant does the point (−7, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  26. 26.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  27. 27.What is the distance between the points (5, 5) and (12, 29)? (a) 26 (b) 31 (c) 625 (d) 25
  28. 28.What is the distance between the points (3, 1) and (10, 25)? (a) 25 (b) 625 (c) 31 (d) 26
  29. 29.What is the midpoint of the line joining (9, 2) and (19, 8)? (a) (14, 5) (b) (5, 14) (c) (5, 3) (d) (28, 10)
  30. 30.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  31. 31.In which quadrant does the point (3, −3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  32. 32.In which quadrant does the point (−3, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  33. 33.What is the distance between the points (0, 2) and (6, 10)? (a) 100 (b) 14 (c) 10 (d) 11
  34. 34.In which quadrant does the point (2, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  35. 35.What is the distance between the points (6, 9) and (15, 21)? (a) 16 (b) 225 (c) 15 (d) 21
  36. 36.What is the midpoint of the line joining (0, 15) and (8, 3)? (a) (4, 9) (b) (9, 4) (c) (4, 6) (d) (8, 18)
  37. 37.In which quadrant does the point (5, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  38. 38.What is the distance between the points (9, 0) and (16, 24)? (a) 26 (b) 31 (c) 625 (d) 25
  39. 39.What is the midpoint of the line joining (8, 1) and (14, 11)? (a) (22, 12) (b) (3, 5) (c) (11, 6) (d) (6, 11)
  40. 40.What is the midpoint of the line joining (0, 6) and (2, 8)? (a) (1, 1) (b) (7, 1) (c) (1, 7) (d) (2, 14)

Answer key

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

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