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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 566 · 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 (5, 10) and (17, 1)? (a) 21 (b) 15 (c) 16 (d) 225
  2. 2.What is the midpoint of the line joining (9, 4) and (13, 6)? (a) (2, 1) (b) (11, 5) (c) (5, 11) (d) (22, 10)
  3. 3.In which quadrant does the point (1, −3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  4. 4.In which quadrant does the point (4, 9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  5. 5.In which quadrant does the point (−1, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  6. 6.In which quadrant does the point (−5, −9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  7. 7.What is the midpoint of the line joining (9, 4) and (19, 0)? (a) (14, 2) (b) (5, 2) (c) (2, 14) (d) (28, 4)
  8. 8.In which quadrant does the point (−6, −7) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  9. 9.What is the midpoint of the line joining (5, 5) and (9, 7)? (a) (6, 7) (b) (14, 12) (c) (2, 1) (d) (7, 6)
  10. 10.What is the distance between the points (2, 17) and (14, 8)? (a) 21 (b) 15 (c) 16 (d) 225
  11. 11.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  12. 12.In which quadrant does the point (−1, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  13. 13.What is the midpoint of the line joining (0, 17) and (2, 5)? (a) (1, 11) (b) (2, 22) (c) (1, 6) (d) (11, 1)
  14. 14.What is the distance between the points (3, 0) and (11, 6)? (a) 10 (b) 11 (c) 100 (d) 14
  15. 15.In which quadrant does the point (−4, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  16. 16.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  17. 17.What is the distance between the points (9, 10) and (15, 2)? (a) 10 (b) 14 (c) 100 (d) 11
  18. 18.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
  19. 19.In which quadrant does the point (1, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  20. 20.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  21. 21.What is the distance between the points (9, 8) and (21, 17)? (a) 16 (b) 21 (c) 15 (d) 225
  22. 22.What is the distance between the points (7, 15) and (13, 7)? (a) 100 (b) 11 (c) 14 (d) 10
  23. 23.What is the midpoint of the line joining (5, 11) and (15, 9)? (a) (20, 20) (b) (11, 10) (c) (5, 1) (d) (10, 10)
  24. 24.In which quadrant does the point (−7, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  25. 25.What is the distance between the points (2, 6) and (10, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  26. 26.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  27. 27.What is the distance between the points (3, 9) and (7, 12)? (a) 25 (b) 5 (c) 6 (d) 7
  28. 28.What is the distance between the points (5, 2) and (17, 18)? (a) 28 (b) 400 (c) 21 (d) 20
  29. 29.What is the midpoint of the line joining (8, 9) and (18, 19)? (a) (26, 28) (b) (14, 13) (c) (13, 14) (d) (5, 5)
  30. 30.In which quadrant does the point (−3, 7) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  31. 31.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  32. 32.In which quadrant does the point (−3, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  33. 33.What is the distance between the points (7, 9) and (13, 1)? (a) 14 (b) 100 (c) 11 (d) 10
  34. 34.In which quadrant does the point (−9, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  35. 35.What is the distance between the points (5, 12) and (17, 7)? (a) 169 (b) 14 (c) 17 (d) 13
  36. 36.In which quadrant does the point (9, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  37. 37.What is the distance between the points (3, 6) and (11, 21)? (a) 23 (b) 17 (c) 18 (d) 289
  38. 38.What is the distance between the points (3, 1) and (7, 4)? (a) 6 (b) 7 (c) 5 (d) 25
  39. 39.What is the midpoint of the line joining (0, 2) and (10, 0)? (a) (10, 2) (b) (1, 5) (c) (5, 1) (d) (6, 1)
  40. 40.What is the distance between the points (6, 6) and (14, 0)? (a) 11 (b) 100 (c) 10 (d) 14

Answer key

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

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