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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 126 · 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 (8, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  2. 2.In which quadrant does the point (3, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  3. 3.What is the distance between the points (1, 9) and (13, 14)? (a) 13 (b) 169 (c) 17 (d) 14
  4. 4.In which quadrant does the point (−1, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  5. 5.What is the midpoint of the line joining (9, 6) and (19, 16)? (a) (14, 11) (b) (28, 22) (c) (11, 14) (d) (5, 5)
  6. 6.In which quadrant does the point (5, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  7. 7.What is the distance between the points (8, 17) and (13, 5)? (a) 169 (b) 13 (c) 14 (d) 17
  8. 8.What is the distance between the points (8, 8) and (11, 12)? (a) 7 (b) 25 (c) 5 (d) 6
  9. 9.In which quadrant does the point (4, 5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  10. 10.What is the distance between the points (3, 12) and (8, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  11. 11.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  12. 12.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  13. 13.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  14. 14.What is the distance between the points (2, 8) and (11, 20)? (a) 21 (b) 15 (c) 16 (d) 225
  15. 15.What is the distance between the points (0, 8) and (9, 20)? (a) 21 (b) 16 (c) 225 (d) 15
  16. 16.In which quadrant does the point (6, 2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  17. 17.In which quadrant does the point (−4, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  18. 18.What is the midpoint of the line joining (4, 8) and (8, 6)? (a) (7, 6) (b) (12, 14) (c) (6, 7) (d) (2, 1)
  19. 19.What is the midpoint of the line joining (1, 6) and (7, 8)? (a) (3, 1) (b) (8, 14) (c) (4, 7) (d) (7, 4)
  20. 20.In which quadrant does the point (−7, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  21. 21.What is the distance between the points (6, 15) and (14, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  22. 22.What is the distance between the points (7, 3) and (11, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  23. 23.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
  24. 24.What is the midpoint of the line joining (7, 15) and (17, 5)? (a) (5, 5) (b) (10, 12) (c) (12, 10) (d) (24, 20)
  25. 25.In which quadrant does the point (5, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.What is the distance between the points (3, 2) and (9, 10)? (a) 14 (b) 10 (c) 100 (d) 11
  27. 27.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  28. 28.What is the distance between the points (4, 2) and (20, 14)? (a) 28 (b) 21 (c) 20 (d) 400
  29. 29.What is the distance between the points (5, 7) and (13, 1)? (a) 100 (b) 10 (c) 14 (d) 11
  30. 30.In which quadrant does the point (6, −1) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  31. 31.What is the midpoint of the line joining (9, 15) and (15, 7)? (a) (11, 12) (b) (3, 4) (c) (12, 11) (d) (24, 22)
  32. 32.In which quadrant does the point (−4, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  33. 33.What is the distance between the points (8, 8) and (32, 1)? (a) 625 (b) 26 (c) 31 (d) 25
  34. 34.What is the midpoint of the line joining (10, 1) and (14, 3)? (a) (2, 1) (b) (12, 2) (c) (24, 4) (d) (2, 12)
  35. 35.In which quadrant does the point (−1, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  36. 36.What is the distance between the points (1, 7) and (9, 22)? (a) 23 (b) 17 (c) 18 (d) 289
  37. 37.What is the distance between the points (6, 2) and (9, 6)? (a) 5 (b) 7 (c) 25 (d) 6
  38. 38.What is the distance between the points (0, 5) and (12, 14)? (a) 16 (b) 15 (c) 225 (d) 21
  39. 39.What is the distance between the points (7, 0) and (14, 24)? (a) 31 (b) 26 (c) 625 (d) 25
  40. 40.What is the midpoint of the line joining (2, 0) and (10, 4)? (a) (2, 6) (b) (6, 2) (c) (12, 4) (d) (4, 2)

Answer key

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

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