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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 593 · 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.In which quadrant does the point (7, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  2. 2.In which quadrant does the point (4, −1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  3. 3.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  4. 4.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  5. 5.What is the distance between the points (4, 6) and (28, 13)? (a) 31 (b) 26 (c) 625 (d) 25
  6. 6.What is the midpoint of the line joining (2, 18) and (14, 6)? (a) (16, 24) (b) (6, 6) (c) (8, 12) (d) (12, 8)
  7. 7.In which quadrant does the point (1, 5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  8. 8.What is the distance between the points (3, 7) and (12, 19)? (a) 16 (b) 21 (c) 15 (d) 225
  9. 9.What is the distance between the points (0, 0) and (3, 4)? (a) 5 (b) 25 (c) 7 (d) 6
  10. 10.What is the distance between the points (0, 15) and (8, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  11. 11.In which quadrant does the point (−1, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  12. 12.What is the midpoint of the line joining (1, 10) and (9, 2)? (a) (10, 12) (b) (5, 6) (c) (6, 5) (d) (4, 4)
  13. 13.What is the midpoint of the line joining (8, 5) and (18, 11)? (a) (26, 16) (b) (5, 3) (c) (8, 13) (d) (13, 8)
  14. 14.What is the midpoint of the line joining (4, 9) and (6, 3)? (a) (1, 3) (b) (5, 6) (c) (10, 12) (d) (6, 5)
  15. 15.What is the distance between the points (8, 10) and (12, 7)? (a) 25 (b) 7 (c) 6 (d) 5
  16. 16.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  17. 17.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  18. 18.What is the midpoint of the line joining (7, 19) and (13, 7)? (a) (10, 13) (b) (20, 26) (c) (13, 10) (d) (3, 6)
  19. 19.In which quadrant does the point (3, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  20. 20.What is the distance between the points (4, 33) and (11, 9)? (a) 26 (b) 625 (c) 31 (d) 25
  21. 21.What is the midpoint of the line joining (7, 7) and (19, 13)? (a) (26, 20) (b) (10, 13) (c) (13, 10) (d) (6, 3)
  22. 22.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  23. 23.What is the midpoint of the line joining (1, 10) and (3, 2)? (a) (6, 2) (b) (4, 12) (c) (2, 6) (d) (1, 4)
  24. 24.What is the midpoint of the line joining (9, 5) and (13, 11)? (a) (2, 3) (b) (11, 8) (c) (22, 16) (d) (8, 11)
  25. 25.What is the midpoint of the line joining (1, 8) and (3, 2)? (a) (2, 5) (b) (1, 3) (c) (4, 10) (d) (5, 2)
  26. 26.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
  27. 27.What is the midpoint of the line joining (5, 15) and (9, 9)? (a) (2, 3) (b) (12, 7) (c) (7, 12) (d) (14, 24)
  28. 28.In which quadrant does the point (4, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  29. 29.In which quadrant does the point (6, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  30. 30.In which quadrant does the point (−3, −9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  31. 31.In which quadrant does the point (2, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  32. 32.In which quadrant does the point (4, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  33. 33.What is the distance between the points (2, 7) and (6, 10)? (a) 7 (b) 5 (c) 6 (d) 25
  34. 34.What is the distance between the points (4, 8) and (7, 12)? (a) 7 (b) 25 (c) 6 (d) 5
  35. 35.What is the midpoint of the line joining (3, 3) and (5, 1)? (a) (2, 4) (b) (8, 4) (c) (4, 2) (d) (1, 1)
  36. 36.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
  37. 37.What is the distance between the points (4, 1) and (12, 16)? (a) 289 (b) 17 (c) 18 (d) 23
  38. 38.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  39. 39.What is the midpoint of the line joining (7, 8) and (13, 16)? (a) (10, 12) (b) (3, 4) (c) (12, 10) (d) (20, 24)
  40. 40.In which quadrant does the point (7, 5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant

Answer key

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

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