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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 446 · 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 (5, 8) and (17, 16)? (a) (6, 4) (b) (12, 11) (c) (11, 12) (d) (22, 24)
  2. 2.What is the midpoint of the line joining (6, 5) and (14, 17)? (a) (10, 11) (b) (11, 10) (c) (20, 22) (d) (4, 6)
  3. 3.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  4. 4.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  5. 5.In which quadrant does the point (−4, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  6. 6.In which quadrant does the point (7, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  7. 7.In which quadrant does the point (1, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  8. 8.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  9. 9.In which quadrant does the point (−8, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  10. 10.What is the distance between the points (7, 5) and (10, 9)? (a) 7 (b) 6 (c) 25 (d) 5
  11. 11.In which quadrant does the point (−7, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  12. 12.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  13. 13.What is the distance between the points (9, 6) and (21, 11)? (a) 17 (b) 14 (c) 169 (d) 13
  14. 14.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  15. 15.In which quadrant does the point (−1, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  16. 16.What is the distance between the points (9, 11) and (17, 5)? (a) 100 (b) 10 (c) 11 (d) 14
  17. 17.What is the distance between the points (6, 7) and (9, 11)? (a) 25 (b) 7 (c) 6 (d) 5
  18. 18.What is the midpoint of the line joining (3, 0) and (5, 12)? (a) (4, 6) (b) (1, 6) (c) (8, 12) (d) (6, 4)
  19. 19.What is the midpoint of the line joining (5, 3) and (13, 11)? (a) (9, 7) (b) (7, 9) (c) (4, 4) (d) (18, 14)
  20. 20.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  21. 21.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
  22. 22.In which quadrant does the point (2, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  23. 23.What is the distance between the points (3, 2) and (11, 8)? (a) 10 (b) 11 (c) 100 (d) 14
  24. 24.What is the midpoint of the line joining (1, 10) and (5, 14)? (a) (12, 3) (b) (2, 2) (c) (3, 12) (d) (6, 24)
  25. 25.In which quadrant does the point (−6, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  26. 26.In which quadrant does the point (7, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  27. 27.What is the distance between the points (4, 1) and (8, 4)? (a) 5 (b) 25 (c) 7 (d) 6
  28. 28.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  29. 29.What is the distance between the points (0, 13) and (9, 1)? (a) 225 (b) 15 (c) 16 (d) 21
  30. 30.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  31. 31.What is the distance between the points (9, 16) and (15, 8)? (a) 14 (b) 10 (c) 100 (d) 11
  32. 32.What is the midpoint of the line joining (2, 19) and (6, 9)? (a) (2, 5) (b) (4, 14) (c) (8, 28) (d) (14, 4)
  33. 33.What is the distance between the points (2, 15) and (10, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  34. 34.What is the midpoint of the line joining (7, 2) and (11, 0)? (a) (2, 1) (b) (9, 1) (c) (18, 2) (d) (1, 9)
  35. 35.What is the distance between the points (8, 4) and (12, 1)? (a) 7 (b) 25 (c) 6 (d) 5
  36. 36.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  37. 37.What is the distance between the points (9, 2) and (25, 14)? (a) 28 (b) 20 (c) 400 (d) 21
  38. 38.In which quadrant does the point (−6, −1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  39. 39.What is the distance between the points (8, 14) and (20, 5)? (a) 225 (b) 16 (c) 15 (d) 21
  40. 40.What is the distance between the points (0, 0) and (12, 5)? (a) 14 (b) 17 (c) 169 (d) 13

Answer key

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

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