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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 956 · 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 (5, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  2. 2.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  3. 3.What is the midpoint of the line joining (9, 9) and (19, 3)? (a) (28, 12) (b) (5, 3) (c) (14, 6) (d) (6, 14)
  4. 4.In which quadrant does the point (−4, −6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  5. 5.In which quadrant does the point (1, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  7. 7.What is the midpoint of the line joining (4, 6) and (16, 8)? (a) (20, 14) (b) (7, 10) (c) (10, 7) (d) (6, 1)
  8. 8.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  9. 9.In which quadrant does the point (−9, −7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  10. 10.In which quadrant does the point (7, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  11. 11.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  12. 12.In which quadrant does the point (−1, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  13. 13.What is the distance between the points (8, 9) and (32, 2)? (a) 31 (b) 25 (c) 26 (d) 625
  14. 14.What is the distance between the points (8, 0) and (14, 8)? (a) 11 (b) 100 (c) 10 (d) 14
  15. 15.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  16. 16.In which quadrant does the point (6, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  17. 17.In which quadrant does the point (8, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  18. 18.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
  19. 19.What is the midpoint of the line joining (0, 11) and (8, 5)? (a) (8, 16) (b) (4, 8) (c) (4, 3) (d) (8, 4)
  20. 20.In which quadrant does the point (1, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  21. 21.What is the midpoint of the line joining (9, 6) and (13, 0)? (a) (3, 11) (b) (22, 6) (c) (2, 3) (d) (11, 3)
  22. 22.In which quadrant does the point (−3, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  23. 23.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  24. 24.What is the midpoint of the line joining (4, 1) and (6, 13)? (a) (1, 6) (b) (5, 7) (c) (7, 5) (d) (10, 14)
  25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  26. 26.What is the distance between the points (1, 5) and (5, 8)? (a) 7 (b) 25 (c) 5 (d) 6
  27. 27.What is the midpoint of the line joining (8, 19) and (10, 9)? (a) (14, 9) (b) (9, 14) (c) (18, 28) (d) (1, 5)
  28. 28.What is the distance between the points (9, 3) and (12, 7)? (a) 5 (b) 6 (c) 25 (d) 7
  29. 29.What is the distance between the points (6, 14) and (14, 8)? (a) 100 (b) 14 (c) 11 (d) 10
  30. 30.In which quadrant does the point (3, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  31. 31.What is the midpoint of the line joining (6, 13) and (10, 5)? (a) (2, 4) (b) (16, 18) (c) (8, 9) (d) (9, 8)
  32. 32.What is the midpoint of the line joining (10, 8) and (12, 18)? (a) (11, 13) (b) (13, 11) (c) (22, 26) (d) (1, 5)
  33. 33.In which quadrant does the point (−1, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  34. 34.In which quadrant does the point (9, −4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  35. 35.What is the midpoint of the line joining (4, 3) and (8, 11)? (a) (6, 7) (b) (2, 4) (c) (12, 14) (d) (7, 6)
  36. 36.In which quadrant does the point (4, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  37. 37.In which quadrant does the point (−4, −7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  38. 38.In which quadrant does the point (−2, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  39. 39.What is the distance between the points (4, 1) and (20, 13)? (a) 21 (b) 20 (c) 400 (d) 28
  40. 40.In which quadrant does the point (2, 9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant

Answer key

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

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