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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 333 · 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, 0) and (18, 9)? (a) 15 (b) 225 (c) 16 (d) 21
  2. 2.What is the midpoint of the line joining (4, 12) and (12, 2)? (a) (16, 14) (b) (8, 7) (c) (7, 8) (d) (4, 5)
  3. 3.What is the distance between the points (6, 9) and (18, 0)? (a) 15 (b) 225 (c) 21 (d) 16
  4. 4.What is the distance between the points (4, 25) and (11, 1)? (a) 25 (b) 26 (c) 31 (d) 625
  5. 5.What is the midpoint of the line joining (8, 0) and (18, 4)? (a) (13, 2) (b) (26, 4) (c) (2, 13) (d) (5, 2)
  6. 6.What is the midpoint of the line joining (4, 7) and (6, 13)? (a) (1, 3) (b) (10, 20) (c) (10, 5) (d) (5, 10)
  7. 7.What is the midpoint of the line joining (5, 12) and (7, 2)? (a) (6, 7) (b) (12, 14) (c) (1, 5) (d) (7, 6)
  8. 8.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  9. 9.What is the midpoint of the line joining (1, 2) and (3, 6)? (a) (4, 2) (b) (4, 8) (c) (2, 4) (d) (1, 2)
  10. 10.What is the distance between the points (7, 6) and (22, 14)? (a) 289 (b) 17 (c) 18 (d) 23
  11. 11.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
  12. 12.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  13. 13.What is the distance between the points (4, 5) and (8, 8)? (a) 6 (b) 7 (c) 5 (d) 25
  14. 14.In which quadrant does the point (7, −4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  15. 15.What is the distance between the points (7, 12) and (11, 9)? (a) 5 (b) 6 (c) 25 (d) 7
  16. 16.What is the midpoint of the line joining (10, 9) and (18, 19)? (a) (14, 14) (b) (4, 5) (c) (15, 14) (d) (28, 28)
  17. 17.What is the midpoint of the line joining (2, 4) and (4, 2)? (a) (4, 3) (b) (6, 6) (c) (3, 3) (d) (1, 1)
  18. 18.What is the distance between the points (6, 8) and (9, 12)? (a) 25 (b) 7 (c) 5 (d) 6
  19. 19.In which quadrant does the point (2, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  20. 20.What is the distance between the points (1, 6) and (9, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  21. 21.In which quadrant does the point (6, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  22. 22.What is the distance between the points (4, 7) and (28, 14)? (a) 25 (b) 26 (c) 31 (d) 625
  23. 23.In which quadrant does the point (−4, −9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  24. 24.What is the midpoint of the line joining (6, 10) and (18, 18)? (a) (12, 14) (b) (24, 28) (c) (6, 4) (d) (14, 12)
  25. 25.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  26. 26.What is the midpoint of the line joining (5, 14) and (13, 6)? (a) (4, 4) (b) (10, 9) (c) (18, 20) (d) (9, 10)
  27. 27.What is the distance between the points (1, 1) and (16, 9)? (a) 23 (b) 289 (c) 18 (d) 17
  28. 28.In which quadrant does the point (−9, 5) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  29. 29.What is the midpoint of the line joining (0, 2) and (2, 0)? (a) (1, 1) (b) (2, 2) (c) (2, 1) (d) (1, 2)
  30. 30.What is the distance between the points (9, 1) and (21, 17)? (a) 20 (b) 400 (c) 28 (d) 21
  31. 31.What is the distance between the points (2, 0) and (8, 8)? (a) 11 (b) 100 (c) 10 (d) 14
  32. 32.In which quadrant does the point (−4, −1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  33. 33.What is the distance between the points (1, 10) and (4, 6)? (a) 6 (b) 7 (c) 25 (d) 5
  34. 34.What is the distance between the points (4, 2) and (13, 14)? (a) 21 (b) 225 (c) 16 (d) 15
  35. 35.In which quadrant does the point (5, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  36. 36.What is the distance between the points (8, 14) and (17, 2)? (a) 16 (b) 21 (c) 15 (d) 225
  37. 37.What is the midpoint of the line joining (1, 10) and (11, 18)? (a) (5, 4) (b) (12, 28) (c) (6, 14) (d) (14, 6)
  38. 38.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  39. 39.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  40. 40.What is the midpoint of the line joining (7, 5) and (13, 7)? (a) (3, 1) (b) (6, 10) (c) (10, 6) (d) (20, 12)

Answer key

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

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