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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 638 · 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 (6, 5) and (30, 12)? (a) 26 (b) 31 (c) 25 (d) 625
  2. 2.What is the midpoint of the line joining (7, 1) and (19, 5)? (a) (13, 3) (b) (26, 6) (c) (3, 13) (d) (6, 2)
  3. 3.What is the distance between the points (9, 6) and (17, 12)? (a) 100 (b) 14 (c) 10 (d) 11
  4. 4.What is the distance between the points (0, 15) and (24, 8)? (a) 625 (b) 26 (c) 25 (d) 31
  5. 5.In which quadrant does the point (2, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  6. 6.What is the distance between the points (7, 5) and (23, 17)? (a) 28 (b) 21 (c) 20 (d) 400
  7. 7.What is the midpoint of the line joining (1, 7) and (3, 15)? (a) (4, 22) (b) (2, 11) (c) (1, 4) (d) (11, 2)
  8. 8.In which quadrant does the point (3, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  9. 9.What is the midpoint of the line joining (0, 0) and (8, 2)? (a) (8, 2) (b) (1, 4) (c) (5, 1) (d) (4, 1)
  10. 10.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
  11. 11.What is the distance between the points (0, 15) and (12, 6)? (a) 225 (b) 21 (c) 16 (d) 15
  12. 12.What is the midpoint of the line joining (6, 0) and (8, 2)? (a) (1, 7) (b) (7, 1) (c) (14, 2) (d) (1, 1)
  13. 13.In which quadrant does the point (−1, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  14. 14.In which quadrant does the point (7, −5) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  15. 15.What is the distance between the points (5, 6) and (17, 15)? (a) 15 (b) 16 (c) 225 (d) 21
  16. 16.In which quadrant does the point (2, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  17. 17.In which quadrant does the point (7, −7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  18. 18.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  19. 19.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
  20. 20.What is the midpoint of the line joining (5, 3) and (15, 15)? (a) (9, 10) (b) (20, 18) (c) (5, 6) (d) (10, 9)
  21. 21.In which quadrant does the point (9, −7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  22. 22.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  23. 23.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
  24. 24.What is the midpoint of the line joining (3, 3) and (5, 9)? (a) (6, 4) (b) (8, 12) (c) (1, 3) (d) (4, 6)
  25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  26. 26.What is the distance between the points (8, 9) and (16, 3)? (a) 14 (b) 100 (c) 10 (d) 11
  27. 27.In which quadrant does the point (1, 4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  28. 28.What is the distance between the points (2, 6) and (14, 1)? (a) 17 (b) 13 (c) 169 (d) 14
  29. 29.What is the midpoint of the line joining (2, 7) and (10, 3)? (a) (12, 10) (b) (4, 2) (c) (6, 5) (d) (5, 6)
  30. 30.What is the midpoint of the line joining (7, 3) and (9, 9)? (a) (16, 12) (b) (6, 8) (c) (1, 3) (d) (8, 6)
  31. 31.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  32. 32.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  33. 33.What is the midpoint of the line joining (7, 11) and (9, 9)? (a) (1, 1) (b) (10, 8) (c) (16, 20) (d) (8, 10)
  34. 34.What is the distance between the points (5, 0) and (8, 4)? (a) 6 (b) 7 (c) 5 (d) 25
  35. 35.In which quadrant does the point (−4, 5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  36. 36.In which quadrant does the point (3, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  37. 37.In which quadrant does the point (9, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  38. 38.In which quadrant does the point (−2, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  39. 39.What is the midpoint of the line joining (2, 10) and (8, 14)? (a) (12, 5) (b) (5, 12) (c) (10, 24) (d) (3, 2)
  40. 40.In which quadrant does the point (−5, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant

Answer key

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

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