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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 739 · 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, 8) and (16, 16)? (a) 289 (b) 18 (c) 17 (d) 23
  2. 2.What is the distance between the points (3, 12) and (6, 8)? (a) 25 (b) 7 (c) 6 (d) 5
  3. 3.What is the midpoint of the line joining (1, 16) and (5, 4)? (a) (6, 20) (b) (10, 3) (c) (3, 10) (d) (2, 6)
  4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
  5. 5.In which quadrant does the point (−1, −1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  6. 6.What is the distance between the points (9, 18) and (18, 6)? (a) 15 (b) 225 (c) 21 (d) 16
  7. 7.What is the distance between the points (6, 7) and (10, 10)? (a) 5 (b) 7 (c) 6 (d) 25
  8. 8.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  9. 9.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  10. 10.What is the distance between the points (6, 10) and (10, 7)? (a) 6 (b) 7 (c) 5 (d) 25
  11. 11.In which quadrant does the point (1, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  12. 12.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  13. 13.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  14. 14.In which quadrant does the point (2, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  15. 15.What is the distance between the points (0, 6) and (4, 9)? (a) 5 (b) 7 (c) 6 (d) 25
  16. 16.What is the distance between the points (2, 15) and (14, 6)? (a) 225 (b) 16 (c) 15 (d) 21
  17. 17.What is the midpoint of the line joining (10, 11) and (18, 5)? (a) (8, 14) (b) (4, 3) (c) (28, 16) (d) (14, 8)
  18. 18.In which quadrant does the point (3, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  19. 19.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  20. 20.In which quadrant does the point (−3, 3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  21. 21.What is the distance between the points (9, 10) and (24, 2)? (a) 17 (b) 18 (c) 23 (d) 289
  22. 22.In which quadrant does the point (−9, 5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  23. 23.What is the distance between the points (1, 6) and (25, 13)? (a) 625 (b) 26 (c) 25 (d) 31
  24. 24.What is the distance between the points (7, 5) and (19, 0)? (a) 13 (b) 17 (c) 14 (d) 169
  25. 25.What is the distance between the points (5, 24) and (13, 9)? (a) 17 (b) 18 (c) 23 (d) 289
  26. 26.In which quadrant does the point (−1, 7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  27. 27.In which quadrant does the point (6, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  28. 28.What is the distance between the points (2, 1) and (6, 4)? (a) 5 (b) 25 (c) 6 (d) 7
  29. 29.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  30. 30.What is the distance between the points (5, 7) and (17, 2)? (a) 14 (b) 169 (c) 17 (d) 13
  31. 31.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  32. 32.In which quadrant does the point (6, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  33. 33.What is the distance between the points (1, 2) and (10, 14)? (a) 225 (b) 15 (c) 21 (d) 16
  34. 34.In which quadrant does the point (−2, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  35. 35.What is the distance between the points (0, 9) and (4, 6)? (a) 6 (b) 5 (c) 7 (d) 25
  36. 36.What is the distance between the points (6, 2) and (15, 14)? (a) 16 (b) 225 (c) 15 (d) 21
  37. 37.What is the distance between the points (2, 12) and (14, 7)? (a) 14 (b) 17 (c) 13 (d) 169
  38. 38.What is the distance between the points (0, 0) and (12, 5)? (a) 14 (b) 169 (c) 17 (d) 13
  39. 39.What is the distance between the points (8, 4) and (12, 1)? (a) 25 (b) 7 (c) 5 (d) 6
  40. 40.What is the distance between the points (8, 0) and (20, 5)? (a) 14 (b) 17 (c) 13 (d) 169

Answer key

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

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