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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 348 · 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.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
  2. 2.What is the midpoint of the line joining (8, 8) and (14, 14)? (a) (11, 11) (b) (12, 11) (c) (3, 3) (d) (22, 22)
  3. 3.What is the distance between the points (5, 6) and (13, 12)? (a) 14 (b) 100 (c) 11 (d) 10
  4. 4.What is the distance between the points (2, 8) and (10, 23)? (a) 23 (b) 18 (c) 17 (d) 289
  5. 5.What is the midpoint of the line joining (1, 2) and (7, 10)? (a) (4, 6) (b) (6, 4) (c) (8, 12) (d) (3, 4)
  6. 6.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
  7. 7.What is the distance between the points (2, 11) and (8, 3)? (a) 14 (b) 11 (c) 100 (d) 10
  8. 8.What is the distance between the points (8, 10) and (20, 1)? (a) 16 (b) 15 (c) 21 (d) 225
  9. 9.What is the midpoint of the line joining (1, 3) and (11, 7)? (a) (6, 5) (b) (5, 2) (c) (5, 6) (d) (12, 10)
  10. 10.What is the distance between the points (7, 1) and (13, 9)? (a) 11 (b) 14 (c) 100 (d) 10
  11. 11.What is the distance between the points (8, 2) and (13, 14)? (a) 14 (b) 17 (c) 169 (d) 13
  12. 12.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  13. 13.In which quadrant does the point (8, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  14. 14.In which quadrant does the point (2, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  15. 15.In which quadrant does the point (1, 9) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  16. 16.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 7 (d) 25
  17. 17.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  18. 18.In which quadrant does the point (−3, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  19. 19.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  20. 20.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
  21. 21.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  22. 22.What is the distance between the points (5, 16) and (20, 8)? (a) 23 (b) 17 (c) 289 (d) 18
  23. 23.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 100 (c) 14 (d) 11
  24. 24.What is the distance between the points (1, 9) and (16, 1)? (a) 23 (b) 17 (c) 18 (d) 289
  25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
  26. 26.What is the distance between the points (7, 18) and (12, 6)? (a) 169 (b) 17 (c) 14 (d) 13
  27. 27.What is the distance between the points (7, 9) and (16, 21)? (a) 21 (b) 15 (c) 16 (d) 225
  28. 28.In which quadrant does the point (−6, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  29. 29.In which quadrant does the point (−1, 3) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  30. 30.What is the distance between the points (3, 19) and (12, 7)? (a) 15 (b) 16 (c) 225 (d) 21
  31. 31.What is the midpoint of the line joining (0, 9) and (12, 13)? (a) (6, 11) (b) (12, 22) (c) (6, 2) (d) (11, 6)
  32. 32.In which quadrant does the point (−4, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  33. 33.In which quadrant does the point (7, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  34. 34.In which quadrant does the point (3, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  35. 35.In which quadrant does the point (−2, 2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  36. 36.What is the midpoint of the line joining (3, 1) and (13, 3)? (a) (5, 1) (b) (8, 2) (c) (2, 8) (d) (16, 4)
  37. 37.What is the distance between the points (8, 21) and (20, 5)? (a) 20 (b) 400 (c) 28 (d) 21
  38. 38.What is the distance between the points (0, 20) and (9, 8)? (a) 225 (b) 21 (c) 15 (d) 16
  39. 39.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  40. 40.What is the distance between the points (1, 2) and (5, 5)? (a) 7 (b) 25 (c) 5 (d) 6

Answer key

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

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