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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 721 · 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 (6, 5) and (16, 17)? (a) (5, 6) (b) (11, 11) (c) (12, 11) (d) (22, 22)
  2. 2.What is the midpoint of the line joining (8, 10) and (12, 2)? (a) (2, 4) (b) (20, 12) (c) (10, 6) (d) (6, 10)
  3. 3.What is the distance between the points (9, 10) and (15, 2)? (a) 100 (b) 14 (c) 11 (d) 10
  4. 4.In which quadrant does the point (−1, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  5. 5.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 14 (c) 17 (d) 169
  6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  7. 7.What is the midpoint of the line joining (9, 7) and (13, 9)? (a) (11, 8) (b) (22, 16) (c) (8, 11) (d) (2, 1)
  8. 8.What is the midpoint of the line joining (6, 17) and (16, 9)? (a) (22, 26) (b) (13, 11) (c) (11, 13) (d) (5, 4)
  9. 9.In which quadrant does the point (−8, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  10. 10.In which quadrant does the point (9, −6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  11. 11.What is the distance between the points (6, 12) and (9, 8)? (a) 6 (b) 7 (c) 25 (d) 5
  12. 12.What is the distance between the points (2, 3) and (10, 9)? (a) 11 (b) 14 (c) 100 (d) 10
  13. 13.What is the midpoint of the line joining (10, 12) and (20, 10)? (a) (30, 22) (b) (15, 11) (c) (5, 1) (d) (11, 15)
  14. 14.What is the distance between the points (4, 11) and (28, 4)? (a) 31 (b) 25 (c) 625 (d) 26
  15. 15.What is the distance between the points (4, 1) and (13, 13)? (a) 21 (b) 15 (c) 16 (d) 225
  16. 16.What is the midpoint of the line joining (0, 22) and (2, 10)? (a) (1, 16) (b) (2, 32) (c) (1, 6) (d) (16, 1)
  17. 17.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  18. 18.What is the midpoint of the line joining (2, 18) and (14, 6)? (a) (12, 8) (b) (16, 24) (c) (6, 6) (d) (8, 12)
  19. 19.In which quadrant does the point (5, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  20. 20.What is the distance between the points (6, 5) and (18, 10)? (a) 13 (b) 169 (c) 14 (d) 17
  21. 21.What is the distance between the points (1, 6) and (16, 14)? (a) 17 (b) 18 (c) 289 (d) 23
  22. 22.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  23. 23.What is the distance between the points (7, 3) and (11, 6)? (a) 7 (b) 25 (c) 5 (d) 6
  24. 24.In which quadrant does the point (2, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  25. 25.What is the midpoint of the line joining (7, 4) and (13, 0)? (a) (10, 2) (b) (20, 4) (c) (2, 10) (d) (3, 2)
  26. 26.In which quadrant does the point (3, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  27. 27.What is the distance between the points (4, 11) and (16, 2)? (a) 225 (b) 16 (c) 21 (d) 15
  28. 28.What is the distance between the points (5, 10) and (13, 4)? (a) 11 (b) 14 (c) 100 (d) 10
  29. 29.What is the midpoint of the line joining (1, 18) and (3, 10)? (a) (14, 2) (b) (1, 4) (c) (4, 28) (d) (2, 14)
  30. 30.In which quadrant does the point (9, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  31. 31.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  32. 32.What is the distance between the points (1, 13) and (6, 1)? (a) 169 (b) 17 (c) 14 (d) 13
  33. 33.What is the midpoint of the line joining (6, 4) and (12, 0)? (a) (18, 4) (b) (3, 2) (c) (2, 9) (d) (9, 2)
  34. 34.What is the distance between the points (9, 14) and (17, 8)? (a) 100 (b) 14 (c) 10 (d) 11
  35. 35.In which quadrant does the point (−9, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  36. 36.In which quadrant does the point (1, 8) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  37. 37.What is the distance between the points (5, 6) and (8, 2)? (a) 25 (b) 5 (c) 7 (d) 6
  38. 38.What is the distance between the points (4, 2) and (8, 5)? (a) 7 (b) 6 (c) 5 (d) 25
  39. 39.In which quadrant does the point (4, 9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  40. 40.In which quadrant does the point (−4, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant

Answer key

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

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