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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 871 · 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 (10, 9) and (18, 1)? (a) (28, 10) (b) (5, 14) (c) (14, 5) (d) (4, 4)
  2. 2.In which quadrant does the point (5, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  3. 3.What is the distance between the points (9, 2) and (16, 26)? (a) 25 (b) 625 (c) 31 (d) 26
  4. 4.What is the distance between the points (9, 13) and (18, 1)? (a) 15 (b) 225 (c) 16 (d) 21
  5. 5.What is the distance between the points (6, 5) and (10, 8)? (a) 25 (b) 6 (c) 7 (d) 5
  6. 6.What is the midpoint of the line joining (8, 15) and (14, 7)? (a) (22, 22) (b) (12, 11) (c) (11, 11) (d) (3, 4)
  7. 7.What is the distance between the points (5, 0) and (14, 12)? (a) 15 (b) 16 (c) 21 (d) 225
  8. 8.In which quadrant does the point (−9, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  9. 9.What is the distance between the points (6, 7) and (14, 1)? (a) 11 (b) 100 (c) 10 (d) 14
  10. 10.What is the distance between the points (4, 7) and (28, 14)? (a) 26 (b) 625 (c) 31 (d) 25
  11. 11.In which quadrant does the point (3, −8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  12. 12.In which quadrant does the point (9, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  13. 13.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  14. 14.What is the midpoint of the line joining (1, 2) and (13, 8)? (a) (6, 3) (b) (7, 5) (c) (5, 7) (d) (14, 10)
  15. 15.What is the distance between the points (0, 8) and (6, 16)? (a) 11 (b) 14 (c) 10 (d) 100
  16. 16.In which quadrant does the point (3, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  17. 17.In which quadrant does the point (3, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  18. 18.What is the distance between the points (1, 14) and (17, 2)? (a) 20 (b) 21 (c) 400 (d) 28
  19. 19.What is the distance between the points (9, 3) and (17, 9)? (a) 11 (b) 10 (c) 14 (d) 100
  20. 20.What is the midpoint of the line joining (5, 2) and (11, 14)? (a) (16, 16) (b) (8, 8) (c) (9, 8) (d) (3, 6)
  21. 21.In which quadrant does the point (−4, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  22. 22.In which quadrant does the point (8, 4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  23. 23.In which quadrant does the point (1, 8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  24. 24.In which quadrant does the point (2, 9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  25. 25.In which quadrant does the point (1, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  26. 26.What is the distance between the points (5, 14) and (21, 2)? (a) 21 (b) 400 (c) 20 (d) 28
  27. 27.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 400 (d) 28
  28. 28.What is the distance between the points (7, 8) and (13, 16)? (a) 11 (b) 100 (c) 10 (d) 14
  29. 29.What is the distance between the points (4, 9) and (12, 24)? (a) 23 (b) 18 (c) 17 (d) 289
  30. 30.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  31. 31.In which quadrant does the point (−9, 9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  32. 32.What is the midpoint of the line joining (9, 8) and (17, 0)? (a) (4, 13) (b) (4, 4) (c) (26, 8) (d) (13, 4)
  33. 33.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  34. 34.In which quadrant does the point (2, 8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  35. 35.In which quadrant does the point (−4, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  36. 36.What is the distance between the points (7, 2) and (16, 14)? (a) 16 (b) 225 (c) 21 (d) 15
  37. 37.What is the distance between the points (7, 19) and (12, 7)? (a) 17 (b) 14 (c) 13 (d) 169
  38. 38.What is the midpoint of the line joining (0, 5) and (2, 7)? (a) (1, 1) (b) (2, 12) (c) (1, 6) (d) (6, 1)
  39. 39.In which quadrant does the point (−8, 9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.What is the midpoint of the line joining (3, 2) and (5, 14)? (a) (1, 6) (b) (4, 8) (c) (8, 16) (d) (8, 4)

Answer key

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

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