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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 189 · 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 (1, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  2. 2.In which quadrant does the point (6, −9) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  3. 3.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  4. 4.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  5. 5.What is the distance between the points (7, 7) and (10, 11)? (a) 25 (b) 7 (c) 5 (d) 6
  6. 6.What is the distance between the points (7, 21) and (19, 5)? (a) 400 (b) 21 (c) 28 (d) 20
  7. 7.What is the distance between the points (0, 6) and (9, 18)? (a) 15 (b) 225 (c) 21 (d) 16
  8. 8.What is the distance between the points (3, 1) and (7, 4)? (a) 7 (b) 6 (c) 25 (d) 5
  9. 9.In which quadrant does the point (9, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  10. 10.What is the distance between the points (8, 8) and (14, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  11. 11.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  12. 12.In which quadrant does the point (7, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  13. 13.In which quadrant does the point (4, 9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  14. 14.In which quadrant does the point (−3, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  15. 15.What is the midpoint of the line joining (7, 18) and (17, 10)? (a) (24, 28) (b) (14, 12) (c) (5, 4) (d) (12, 14)
  16. 16.In which quadrant does the point (−2, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  17. 17.What is the distance between the points (6, 5) and (12, 13)? (a) 10 (b) 100 (c) 11 (d) 14
  18. 18.What is the distance between the points (9, 9) and (18, 21)? (a) 16 (b) 225 (c) 15 (d) 21
  19. 19.In which quadrant does the point (7, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  20. 20.What is the distance between the points (9, 19) and (21, 3)? (a) 28 (b) 21 (c) 20 (d) 400
  21. 21.What is the midpoint of the line joining (1, 14) and (7, 2)? (a) (8, 4) (b) (3, 6) (c) (4, 8) (d) (8, 16)
  22. 22.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  23. 23.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  24. 24.What is the distance between the points (4, 4) and (12, 10)? (a) 14 (b) 11 (c) 10 (d) 100
  25. 25.In which quadrant does the point (−3, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  26. 26.In which quadrant does the point (−3, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  27. 27.What is the midpoint of the line joining (5, 14) and (7, 4)? (a) (1, 5) (b) (6, 9) (c) (9, 6) (d) (12, 18)
  28. 28.In which quadrant does the point (−1, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  29. 29.What is the midpoint of the line joining (9, 8) and (17, 20)? (a) (26, 28) (b) (13, 14) (c) (4, 6) (d) (14, 13)
  30. 30.In which quadrant does the point (−7, −2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  31. 31.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  32. 32.In which quadrant does the point (−2, 4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  33. 33.In which quadrant does the point (−6, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  34. 34.In which quadrant does the point (5, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  35. 35.In which quadrant does the point (−1, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  36. 36.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
  37. 37.In which quadrant does the point (−8, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  38. 38.In which quadrant does the point (3, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  39. 39.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  40. 40.In which quadrant does the point (9, 9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant

Answer key

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

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