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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 857 · 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 (1, 14) and (9, 8)? (a) 14 (b) 10 (c) 100 (d) 11
  2. 2.What is the midpoint of the line joining (3, 22) and (15, 10)? (a) (9, 16) (b) (6, 6) (c) (16, 9) (d) (18, 32)
  3. 3.What is the distance between the points (8, 5) and (16, 20)? (a) 17 (b) 18 (c) 23 (d) 289
  4. 4.What is the distance between the points (1, 0) and (7, 8)? (a) 14 (b) 10 (c) 11 (d) 100
  5. 5.In which quadrant does the point (4, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  6. 6.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  7. 7.What is the distance between the points (8, 7) and (32, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  8. 8.What is the distance between the points (0, 9) and (12, 18)? (a) 15 (b) 16 (c) 21 (d) 225
  9. 9.What is the distance between the points (6, 29) and (13, 5)? (a) 625 (b) 25 (c) 31 (d) 26
  10. 10.What is the distance between the points (3, 3) and (7, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  11. 11.In which quadrant does the point (2, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  12. 12.What is the distance between the points (2, 0) and (5, 4)? (a) 6 (b) 5 (c) 7 (d) 25
  13. 13.What is the midpoint of the line joining (1, 7) and (11, 1)? (a) (12, 8) (b) (4, 6) (c) (5, 3) (d) (6, 4)
  14. 14.What is the distance between the points (1, 3) and (9, 18)? (a) 23 (b) 18 (c) 17 (d) 289
  15. 15.What is the distance between the points (3, 11) and (27, 4)? (a) 625 (b) 26 (c) 31 (d) 25
  16. 16.In which quadrant does the point (−1, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  17. 17.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  18. 18.What is the distance between the points (7, 30) and (14, 6)? (a) 625 (b) 26 (c) 31 (d) 25
  19. 19.What is the midpoint of the line joining (2, 14) and (4, 6)? (a) (1, 4) (b) (10, 3) (c) (3, 10) (d) (6, 20)
  20. 20.What is the distance between the points (2, 16) and (14, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  21. 21.What is the distance between the points (8, 3) and (14, 11)? (a) 14 (b) 100 (c) 11 (d) 10
  22. 22.What is the midpoint of the line joining (6, 9) and (16, 5)? (a) (5, 2) (b) (22, 14) (c) (7, 11) (d) (11, 7)
  23. 23.What is the midpoint of the line joining (2, 5) and (12, 13)? (a) (7, 9) (b) (14, 18) (c) (5, 4) (d) (9, 7)
  24. 24.What is the midpoint of the line joining (0, 11) and (2, 1)? (a) (2, 12) (b) (1, 5) (c) (6, 1) (d) (1, 6)
  25. 25.What is the midpoint of the line joining (1, 15) and (3, 7)? (a) (11, 2) (b) (1, 4) (c) (4, 22) (d) (2, 11)
  26. 26.What is the distance between the points (6, 2) and (11, 14)? (a) 169 (b) 14 (c) 13 (d) 17
  27. 27.What is the distance between the points (5, 7) and (13, 1)? (a) 10 (b) 100 (c) 11 (d) 14
  28. 28.In which quadrant does the point (−4, −5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  29. 29.What is the distance between the points (3, 7) and (9, 15)? (a) 11 (b) 10 (c) 14 (d) 100
  30. 30.What is the distance between the points (2, 0) and (11, 12)? (a) 21 (b) 16 (c) 225 (d) 15
  31. 31.In which quadrant does the point (8, −8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  32. 32.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  33. 33.In which quadrant does the point (5, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  34. 34.What is the distance between the points (1, 9) and (9, 24)? (a) 23 (b) 17 (c) 18 (d) 289
  35. 35.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  36. 36.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  37. 37.What is the midpoint of the line joining (1, 6) and (3, 0)? (a) (3, 2) (b) (4, 6) (c) (2, 3) (d) (1, 3)
  38. 38.In which quadrant does the point (−6, 5) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  39. 39.What is the distance between the points (8, 2) and (20, 11)? (a) 225 (b) 15 (c) 21 (d) 16
  40. 40.What is the midpoint of the line joining (7, 7) and (19, 5)? (a) (6, 1) (b) (6, 13) (c) (13, 6) (d) (26, 12)

Answer key

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

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