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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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