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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 244 · 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.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  2. 2.In which quadrant does the point (−2, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  3. 3.What is the midpoint of the line joining (0, 1) and (6, 3)? (a) (2, 3) (b) (3, 1) (c) (6, 4) (d) (3, 2)
  4. 4.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  5. 5.What is the midpoint of the line joining (6, 9) and (12, 5)? (a) (18, 14) (b) (9, 7) (c) (7, 9) (d) (3, 2)
  6. 6.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  7. 7.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  8. 8.What is the midpoint of the line joining (2, 5) and (12, 11)? (a) (7, 8) (b) (8, 7) (c) (14, 16) (d) (5, 3)
  9. 9.In which quadrant does the point (4, 7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  10. 10.What is the midpoint of the line joining (4, 7) and (16, 13)? (a) (11, 10) (b) (10, 10) (c) (20, 20) (d) (6, 3)
  11. 11.What is the distance between the points (3, 6) and (6, 2)? (a) 25 (b) 7 (c) 6 (d) 5
  12. 12.In which quadrant does the point (1, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  13. 13.What is the midpoint of the line joining (0, 13) and (8, 3)? (a) (4, 5) (b) (4, 8) (c) (8, 16) (d) (8, 4)
  14. 14.What is the midpoint of the line joining (7, 9) and (17, 19)? (a) (5, 5) (b) (14, 12) (c) (12, 14) (d) (24, 28)
  15. 15.What is the distance between the points (7, 17) and (19, 1)? (a) 28 (b) 20 (c) 21 (d) 400
  16. 16.In which quadrant does the point (5, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  17. 17.What is the midpoint of the line joining (3, 6) and (7, 2)? (a) (10, 8) (b) (4, 5) (c) (2, 2) (d) (5, 4)
  18. 18.What is the distance between the points (8, 2) and (20, 18)? (a) 21 (b) 400 (c) 28 (d) 20
  19. 19.What is the distance between the points (1, 2) and (4, 6)? (a) 25 (b) 6 (c) 7 (d) 5
  20. 20.In which quadrant does the point (3, −8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  21. 21.What is the midpoint of the line joining (7, 9) and (15, 5)? (a) (22, 14) (b) (7, 11) (c) (11, 7) (d) (4, 2)
  22. 22.In which quadrant does the point (7, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  23. 23.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  24. 24.What is the distance between the points (4, 5) and (7, 1)? (a) 25 (b) 5 (c) 7 (d) 6
  25. 25.In which quadrant does the point (4, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  26. 26.What is the distance between the points (3, 15) and (9, 7)? (a) 100 (b) 14 (c) 11 (d) 10
  27. 27.What is the distance between the points (1, 8) and (7, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  28. 28.In which quadrant does the point (4, −1) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  29. 29.In which quadrant does the point (−7, 9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  30. 30.What is the midpoint of the line joining (4, 15) and (14, 5)? (a) (18, 20) (b) (5, 5) (c) (10, 9) (d) (9, 10)
  31. 31.What is the midpoint of the line joining (2, 0) and (8, 12)? (a) (10, 12) (b) (3, 6) (c) (5, 6) (d) (6, 5)
  32. 32.What is the distance between the points (3, 5) and (15, 21)? (a) 20 (b) 400 (c) 28 (d) 21
  33. 33.What is the distance between the points (9, 24) and (16, 0)? (a) 25 (b) 625 (c) 26 (d) 31
  34. 34.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 23 (d) 18
  35. 35.What is the distance between the points (6, 2) and (14, 8)? (a) 11 (b) 100 (c) 10 (d) 14
  36. 36.In which quadrant does the point (7, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  37. 37.What is the midpoint of the line joining (10, 9) and (14, 5)? (a) (12, 7) (b) (7, 12) (c) (24, 14) (d) (2, 2)
  38. 38.In which quadrant does the point (−3, −2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  39. 39.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
  40. 40.In which quadrant does the point (6, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant

Answer key

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

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