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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 91 · 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 (8, 8) and (14, 6)? (a) (22, 14) (b) (3, 1) (c) (7, 11) (d) (11, 7)
  2. 2.What is the midpoint of the line joining (5, 3) and (13, 9)? (a) (18, 12) (b) (9, 6) (c) (6, 9) (d) (4, 3)
  3. 3.In which quadrant does the point (8, −3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  4. 4.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  5. 5.What is the midpoint of the line joining (9, 10) and (17, 14)? (a) (13, 12) (b) (12, 13) (c) (4, 2) (d) (26, 24)
  6. 6.What is the midpoint of the line joining (6, 21) and (16, 9)? (a) (22, 30) (b) (5, 6) (c) (11, 15) (d) (15, 11)
  7. 7.What is the distance between the points (8, 4) and (11, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  8. 8.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  9. 9.What is the midpoint of the line joining (1, 7) and (7, 9)? (a) (8, 16) (b) (8, 4) (c) (4, 8) (d) (3, 1)
  10. 10.What is the midpoint of the line joining (0, 5) and (2, 7)? (a) (2, 12) (b) (6, 1) (c) (1, 6) (d) (1, 1)
  11. 11.What is the distance between the points (2, 9) and (26, 2)? (a) 31 (b) 25 (c) 625 (d) 26
  12. 12.What is the midpoint of the line joining (4, 6) and (16, 18)? (a) (12, 10) (b) (6, 6) (c) (10, 12) (d) (20, 24)
  13. 13.In which quadrant does the point (3, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  14. 14.What is the distance between the points (2, 1) and (10, 16)? (a) 18 (b) 289 (c) 17 (d) 23
  15. 15.In which quadrant does the point (−9, 7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  16. 16.What is the distance between the points (6, 25) and (13, 1)? (a) 25 (b) 31 (c) 625 (d) 26
  17. 17.In which quadrant does the point (8, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  18. 18.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  19. 19.What is the distance between the points (7, 6) and (10, 2)? (a) 5 (b) 7 (c) 6 (d) 25
  20. 20.What is the distance between the points (2, 13) and (17, 5)? (a) 23 (b) 17 (c) 289 (d) 18
  21. 21.In which quadrant does the point (5, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  22. 22.In which quadrant does the point (−8, −7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  23. 23.What is the distance between the points (4, 5) and (7, 1)? (a) 7 (b) 6 (c) 5 (d) 25
  24. 24.What is the distance between the points (6, 9) and (9, 5)? (a) 25 (b) 6 (c) 5 (d) 7
  25. 25.In which quadrant does the point (7, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.In which quadrant does the point (−6, −9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  27. 27.What is the distance between the points (7, 13) and (19, 8)? (a) 13 (b) 17 (c) 169 (d) 14
  28. 28.What is the midpoint of the line joining (3, 19) and (11, 7)? (a) (4, 6) (b) (14, 26) (c) (7, 13) (d) (13, 7)
  29. 29.What is the distance between the points (9, 7) and (18, 19)? (a) 15 (b) 21 (c) 225 (d) 16
  30. 30.In which quadrant does the point (7, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  31. 31.What is the distance between the points (0, 6) and (3, 2)? (a) 6 (b) 7 (c) 25 (d) 5
  32. 32.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 289 (c) 18 (d) 23
  33. 33.In which quadrant does the point (6, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  34. 34.In which quadrant does the point (4, −9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  35. 35.What is the distance between the points (0, 2) and (8, 17)? (a) 23 (b) 17 (c) 289 (d) 18
  36. 36.What is the distance between the points (6, 0) and (15, 12)? (a) 21 (b) 225 (c) 16 (d) 15
  37. 37.What is the distance between the points (6, 14) and (22, 2)? (a) 28 (b) 21 (c) 20 (d) 400
  38. 38.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
  39. 39.What is the midpoint of the line joining (5, 5) and (11, 11)? (a) (9, 8) (b) (16, 16) (c) (8, 8) (d) (3, 3)
  40. 40.What is the midpoint of the line joining (4, 16) and (8, 4)? (a) (12, 20) (b) (2, 6) (c) (6, 10) (d) (10, 6)

Answer key

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

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