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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 212 · 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.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 169 (c) 14 (d) 17
  2. 2.In which quadrant does the point (4, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  3. 3.What is the midpoint of the line joining (3, 13) and (5, 1)? (a) (7, 4) (b) (8, 14) (c) (4, 7) (d) (1, 6)
  4. 4.What is the distance between the points (4, 3) and (16, 12)? (a) 225 (b) 15 (c) 16 (d) 21
  5. 5.In which quadrant does the point (2, −5) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  6. 6.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  7. 7.What is the distance between the points (3, 5) and (15, 14)? (a) 16 (b) 15 (c) 21 (d) 225
  8. 8.What is the midpoint of the line joining (4, 0) and (14, 8)? (a) (5, 4) (b) (4, 9) (c) (9, 4) (d) (18, 8)
  9. 9.What is the midpoint of the line joining (1, 12) and (11, 8)? (a) (10, 6) (b) (5, 2) (c) (12, 20) (d) (6, 10)
  10. 10.In which quadrant does the point (−5, 3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  11. 11.What is the distance between the points (4, 7) and (12, 22)? (a) 23 (b) 17 (c) 18 (d) 289
  12. 12.In which quadrant does the point (−9, −6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  13. 13.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  14. 14.What is the distance between the points (7, 6) and (15, 12)? (a) 14 (b) 100 (c) 11 (d) 10
  15. 15.In which quadrant does the point (8, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  16. 16.In which quadrant does the point (1, −8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  17. 17.What is the distance between the points (6, 4) and (14, 19)? (a) 18 (b) 289 (c) 17 (d) 23
  18. 18.In which quadrant does the point (−3, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  19. 19.What is the distance between the points (7, 5) and (12, 17)? (a) 169 (b) 17 (c) 14 (d) 13
  20. 20.In which quadrant does the point (6, −3) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  21. 21.In which quadrant does the point (1, 8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  22. 22.In which quadrant does the point (−8, 8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  23. 23.What is the distance between the points (1, 1) and (17, 13)? (a) 28 (b) 400 (c) 20 (d) 21
  24. 24.What is the distance between the points (0, 2) and (15, 10)? (a) 18 (b) 17 (c) 289 (d) 23
  25. 25.What is the distance between the points (1, 7) and (25, 14)? (a) 625 (b) 25 (c) 31 (d) 26
  26. 26.What is the distance between the points (5, 8) and (9, 5)? (a) 25 (b) 5 (c) 6 (d) 7
  27. 27.What is the midpoint of the line joining (3, 1) and (13, 3)? (a) (5, 1) (b) (2, 8) (c) (16, 4) (d) (8, 2)
  28. 28.In which quadrant does the point (−5, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  29. 29.What is the midpoint of the line joining (2, 3) and (4, 1)? (a) (1, 1) (b) (6, 4) (c) (3, 2) (d) (2, 3)
  30. 30.What is the midpoint of the line joining (9, 5) and (15, 9)? (a) (7, 12) (b) (3, 2) (c) (24, 14) (d) (12, 7)
  31. 31.What is the midpoint of the line joining (6, 14) and (8, 4)? (a) (9, 7) (b) (14, 18) (c) (7, 9) (d) (1, 5)
  32. 32.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  33. 33.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  34. 34.In which quadrant does the point (−5, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  35. 35.In which quadrant does the point (−1, 5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  36. 36.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  37. 37.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  38. 38.What is the distance between the points (8, 6) and (20, 22)? (a) 20 (b) 21 (c) 400 (d) 28
  39. 39.In which quadrant does the point (−1, 4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  40. 40.In which quadrant does the point (9, −4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant

Answer key

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

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