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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 275 · 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 (7, 4) and (17, 0)? (a) (12, 2) (b) (2, 12) (c) (5, 2) (d) (24, 4)
  2. 2.What is the distance between the points (6, 4) and (9, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  3. 3.In which quadrant does the point (3, −7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  4. 4.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  5. 5.What is the midpoint of the line joining (3, 5) and (9, 1)? (a) (3, 6) (b) (6, 3) (c) (12, 6) (d) (3, 2)
  6. 6.What is the distance between the points (0, 3) and (12, 19)? (a) 400 (b) 20 (c) 21 (d) 28
  7. 7.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 16 (d) 21
  8. 8.What is the midpoint of the line joining (9, 2) and (19, 10)? (a) (28, 12) (b) (6, 14) (c) (14, 6) (d) (5, 4)
  9. 9.What is the distance between the points (1, 18) and (9, 3)? (a) 18 (b) 23 (c) 289 (d) 17
  10. 10.What is the midpoint of the line joining (0, 8) and (8, 20)? (a) (4, 6) (b) (14, 4) (c) (4, 14) (d) (8, 28)
  11. 11.What is the midpoint of the line joining (5, 1) and (9, 11)? (a) (2, 5) (b) (14, 12) (c) (6, 7) (d) (7, 6)
  12. 12.What is the midpoint of the line joining (0, 7) and (4, 15)? (a) (4, 22) (b) (2, 4) (c) (2, 11) (d) (11, 2)
  13. 13.In which quadrant does the point (9, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  14. 14.What is the distance between the points (5, 9) and (17, 18)? (a) 15 (b) 21 (c) 16 (d) 225
  15. 15.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  16. 16.What is the distance between the points (7, 5) and (19, 0)? (a) 13 (b) 169 (c) 14 (d) 17
  17. 17.What is the midpoint of the line joining (2, 3) and (12, 1)? (a) (5, 1) (b) (14, 4) (c) (7, 2) (d) (2, 7)
  18. 18.What is the distance between the points (2, 14) and (10, 8)? (a) 11 (b) 14 (c) 10 (d) 100
  19. 19.What is the distance between the points (5, 7) and (14, 19)? (a) 15 (b) 225 (c) 16 (d) 21
  20. 20.In which quadrant does the point (−2, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  21. 21.What is the distance between the points (7, 24) and (14, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  22. 22.What is the distance between the points (3, 11) and (7, 8)? (a) 25 (b) 5 (c) 6 (d) 7
  23. 23.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  24. 24.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  25. 25.What is the midpoint of the line joining (8, 3) and (16, 5)? (a) (4, 12) (b) (24, 8) (c) (12, 4) (d) (4, 1)
  26. 26.In which quadrant does the point (3, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  27. 27.What is the distance between the points (8, 0) and (20, 5)? (a) 17 (b) 169 (c) 13 (d) 14
  28. 28.What is the distance between the points (2, 5) and (10, 11)? (a) 14 (b) 100 (c) 11 (d) 10
  29. 29.What is the midpoint of the line joining (0, 4) and (10, 6)? (a) (6, 5) (b) (5, 5) (c) (5, 1) (d) (10, 10)
  30. 30.What is the midpoint of the line joining (3, 3) and (15, 1)? (a) (18, 4) (b) (6, 1) (c) (2, 9) (d) (9, 2)
  31. 31.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  32. 32.What is the distance between the points (6, 12) and (12, 4)? (a) 14 (b) 11 (c) 10 (d) 100
  33. 33.What is the midpoint of the line joining (2, 1) and (14, 5)? (a) (3, 8) (b) (6, 2) (c) (16, 6) (d) (8, 3)
  34. 34.What is the distance between the points (6, 11) and (18, 6)? (a) 17 (b) 14 (c) 169 (d) 13
  35. 35.In which quadrant does the point (−7, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  36. 36.In which quadrant does the point (9, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  37. 37.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  38. 38.What is the distance between the points (3, 8) and (11, 23)? (a) 17 (b) 289 (c) 23 (d) 18
  39. 39.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  40. 40.In which quadrant does the point (3, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant

Answer key

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

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