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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 76 · 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 (2, 0) and (10, 6)? (a) 11 (b) 14 (c) 100 (d) 10
  2. 2.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  3. 3.What is the distance between the points (1, 13) and (13, 4)? (a) 15 (b) 225 (c) 21 (d) 16
  4. 4.What is the distance between the points (2, 2) and (5, 6)? (a) 6 (b) 7 (c) 5 (d) 25
  5. 5.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  6. 6.What is the distance between the points (3, 6) and (10, 30)? (a) 31 (b) 25 (c) 26 (d) 625
  7. 7.What is the midpoint of the line joining (7, 0) and (17, 6)? (a) (12, 3) (b) (24, 6) (c) (3, 12) (d) (5, 3)
  8. 8.What is the distance between the points (1, 8) and (9, 14)? (a) 11 (b) 10 (c) 100 (d) 14
  9. 9.What is the distance between the points (6, 17) and (18, 8)? (a) 21 (b) 15 (c) 16 (d) 225
  10. 10.In which quadrant does the point (2, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  11. 11.What is the distance between the points (1, 6) and (4, 10)? (a) 6 (b) 25 (c) 5 (d) 7
  12. 12.What is the distance between the points (1, 3) and (10, 15)? (a) 15 (b) 21 (c) 16 (d) 225
  13. 13.What is the midpoint of the line joining (0, 9) and (2, 3)? (a) (6, 1) (b) (1, 3) (c) (1, 6) (d) (2, 12)
  14. 14.What is the distance between the points (0, 13) and (5, 1)? (a) 169 (b) 13 (c) 17 (d) 14
  15. 15.What is the midpoint of the line joining (8, 8) and (14, 14)? (a) (11, 11) (b) (3, 3) (c) (12, 11) (d) (22, 22)
  16. 16.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 17 (d) 14
  17. 17.What is the distance between the points (0, 3) and (5, 15)? (a) 14 (b) 13 (c) 169 (d) 17
  18. 18.What is the midpoint of the line joining (3, 11) and (13, 3)? (a) (16, 14) (b) (8, 7) (c) (7, 8) (d) (5, 4)
  19. 19.What is the distance between the points (8, 6) and (32, 13)? (a) 31 (b) 625 (c) 25 (d) 26
  20. 20.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  21. 21.In which quadrant does the point (−6, 4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  22. 22.What is the distance between the points (6, 15) and (14, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  23. 23.What is the distance between the points (1, 19) and (13, 3)? (a) 28 (b) 20 (c) 21 (d) 400
  24. 24.What is the midpoint of the line joining (3, 18) and (7, 6)? (a) (5, 12) (b) (10, 24) (c) (2, 6) (d) (12, 5)
  25. 25.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  26. 26.In which quadrant does the point (5, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  27. 27.What is the distance between the points (1, 7) and (25, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  28. 28.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 5 (c) 25 (d) 7
  29. 29.In which quadrant does the point (7, 2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  30. 30.In which quadrant does the point (−6, −7) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  31. 31.What is the midpoint of the line joining (7, 3) and (11, 13)? (a) (9, 8) (b) (8, 9) (c) (2, 5) (d) (18, 16)
  32. 32.What is the midpoint of the line joining (8, 1) and (12, 9)? (a) (5, 10) (b) (10, 5) (c) (2, 4) (d) (20, 10)
  33. 33.What is the distance between the points (8, 15) and (32, 8)? (a) 26 (b) 25 (c) 31 (d) 625
  34. 34.What is the distance between the points (9, 11) and (13, 8)? (a) 25 (b) 7 (c) 5 (d) 6
  35. 35.What is the distance between the points (1, 1) and (13, 6)? (a) 17 (b) 13 (c) 169 (d) 14
  36. 36.What is the midpoint of the line joining (0, 10) and (12, 6)? (a) (12, 16) (b) (6, 8) (c) (6, 2) (d) (8, 6)
  37. 37.What is the midpoint of the line joining (3, 1) and (11, 5)? (a) (7, 3) (b) (3, 7) (c) (14, 6) (d) (4, 2)
  38. 38.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
  39. 39.What is the distance between the points (0, 10) and (3, 6)? (a) 7 (b) 25 (c) 6 (d) 5
  40. 40.In which quadrant does the point (7, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant

Answer key

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

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