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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 106 · 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 midpoint of the line joining (1, 8) and (13, 6)? (a) (8, 7) (b) (14, 14) (c) (6, 1) (d) (7, 7)
  2. 2.In which quadrant does the point (1, 4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  3. 3.In which quadrant does the point (−7, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  4. 4.What is the distance between the points (4, 8) and (28, 1)? (a) 625 (b) 26 (c) 31 (d) 25
  5. 5.What is the distance between the points (6, 3) and (14, 9)? (a) 14 (b) 100 (c) 10 (d) 11
  6. 6.In which quadrant does the point (−5, −9) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  7. 7.What is the midpoint of the line joining (8, 4) and (12, 16)? (a) (20, 20) (b) (2, 6) (c) (11, 10) (d) (10, 10)
  8. 8.In which quadrant does the point (4, 5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  9. 9.In which quadrant does the point (−8, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  10. 10.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  11. 11.What is the distance between the points (8, 13) and (16, 7)? (a) 100 (b) 10 (c) 14 (d) 11
  12. 12.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
  13. 13.In which quadrant does the point (9, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  14. 14.In which quadrant does the point (−6, −5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  15. 15.What is the midpoint of the line joining (1, 11) and (7, 1)? (a) (6, 4) (b) (4, 6) (c) (3, 5) (d) (8, 12)
  16. 16.In which quadrant does the point (5, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  17. 17.What is the midpoint of the line joining (3, 10) and (9, 18)? (a) (12, 28) (b) (14, 6) (c) (3, 4) (d) (6, 14)
  18. 18.In which quadrant does the point (−2, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  19. 19.What is the midpoint of the line joining (9, 17) and (13, 5)? (a) (2, 6) (b) (11, 11) (c) (22, 22) (d) (12, 11)
  20. 20.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  21. 21.What is the midpoint of the line joining (1, 1) and (3, 11)? (a) (6, 2) (b) (1, 5) (c) (4, 12) (d) (2, 6)
  22. 22.In which quadrant does the point (−4, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  23. 23.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  24. 24.In which quadrant does the point (3, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  25. 25.What is the distance between the points (3, 0) and (7, 3)? (a) 7 (b) 25 (c) 5 (d) 6
  26. 26.In which quadrant does the point (−5, −2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  27. 27.What is the distance between the points (7, 17) and (13, 9)? (a) 100 (b) 10 (c) 11 (d) 14
  28. 28.What is the midpoint of the line joining (9, 0) and (13, 12)? (a) (11, 6) (b) (2, 6) (c) (6, 11) (d) (22, 12)
  29. 29.What is the distance between the points (9, 0) and (17, 6)? (a) 10 (b) 100 (c) 14 (d) 11
  30. 30.What is the distance between the points (2, 19) and (14, 3)? (a) 20 (b) 28 (c) 21 (d) 400
  31. 31.In which quadrant does the point (−8, −6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  32. 32.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 7 (c) 5 (d) 6
  33. 33.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
  34. 34.What is the distance between the points (0, 7) and (4, 10)? (a) 6 (b) 5 (c) 25 (d) 7
  35. 35.What is the distance between the points (4, 0) and (10, 8)? (a) 14 (b) 10 (c) 100 (d) 11
  36. 36.What is the distance between the points (8, 7) and (20, 2)? (a) 169 (b) 13 (c) 17 (d) 14
  37. 37.What is the distance between the points (0, 24) and (7, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  38. 38.What is the distance between the points (2, 5) and (14, 14)? (a) 225 (b) 15 (c) 16 (d) 21
  39. 39.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  40. 40.In which quadrant does the point (−8, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant

Answer key

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

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