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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 68 · 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 (6, 12) and (21, 4)? (a) 17 (b) 289 (c) 18 (d) 23
  2. 2.What is the distance between the points (1, 6) and (4, 2)? (a) 6 (b) 5 (c) 7 (d) 25
  3. 3.What is the distance between the points (6, 10) and (14, 4)? (a) 100 (b) 10 (c) 14 (d) 11
  4. 4.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  5. 5.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  6. 6.What is the midpoint of the line joining (7, 18) and (9, 6)? (a) (1, 6) (b) (16, 24) (c) (12, 8) (d) (8, 12)
  7. 7.What is the distance between the points (9, 4) and (14, 16)? (a) 13 (b) 169 (c) 14 (d) 17
  8. 8.What is the midpoint of the line joining (9, 17) and (11, 5)? (a) (1, 6) (b) (20, 22) (c) (11, 10) (d) (10, 11)
  9. 9.What is the distance between the points (8, 7) and (13, 19)? (a) 169 (b) 17 (c) 14 (d) 13
  10. 10.What is the distance between the points (1, 5) and (10, 17)? (a) 16 (b) 21 (c) 15 (d) 225
  11. 11.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  12. 12.In which quadrant does the point (3, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  13. 13.What is the distance between the points (2, 1) and (17, 9)? (a) 23 (b) 17 (c) 289 (d) 18
  14. 14.In which quadrant does the point (3, −4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  15. 15.What is the midpoint of the line joining (7, 7) and (9, 19)? (a) (8, 13) (b) (1, 6) (c) (13, 8) (d) (16, 26)
  16. 16.What is the distance between the points (9, 5) and (12, 9)? (a) 6 (b) 7 (c) 25 (d) 5
  17. 17.What is the midpoint of the line joining (1, 12) and (5, 6)? (a) (3, 9) (b) (2, 3) (c) (9, 3) (d) (6, 18)
  18. 18.In which quadrant does the point (−3, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  19. 19.What is the distance between the points (3, 4) and (11, 10)? (a) 10 (b) 14 (c) 100 (d) 11
  20. 20.What is the distance between the points (5, 0) and (13, 6)? (a) 100 (b) 14 (c) 10 (d) 11
  21. 21.What is the distance between the points (3, 9) and (11, 15)? (a) 14 (b) 10 (c) 11 (d) 100
  22. 22.In which quadrant does the point (−7, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  23. 23.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  24. 24.What is the distance between the points (1, 0) and (16, 8)? (a) 17 (b) 23 (c) 18 (d) 289
  25. 25.In which quadrant does the point (2, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  26. 26.What is the distance between the points (5, 5) and (14, 17)? (a) 225 (b) 21 (c) 15 (d) 16
  27. 27.What is the distance between the points (7, 6) and (19, 22)? (a) 21 (b) 400 (c) 20 (d) 28
  28. 28.What is the midpoint of the line joining (9, 7) and (15, 17)? (a) (3, 5) (b) (24, 24) (c) (13, 12) (d) (12, 12)
  29. 29.What is the distance between the points (8, 4) and (20, 13)? (a) 21 (b) 15 (c) 16 (d) 225
  30. 30.What is the midpoint of the line joining (4, 1) and (16, 7)? (a) (10, 4) (b) (4, 10) (c) (6, 3) (d) (20, 8)
  31. 31.In which quadrant does the point (4, 3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  32. 32.What is the distance between the points (8, 5) and (20, 10)? (a) 17 (b) 14 (c) 13 (d) 169
  33. 33.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  34. 34.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
  35. 35.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  36. 36.In which quadrant does the point (−6, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  37. 37.What is the midpoint of the line joining (4, 2) and (10, 4)? (a) (14, 6) (b) (3, 7) (c) (7, 3) (d) (3, 1)
  38. 38.What is the midpoint of the line joining (8, 5) and (14, 13)? (a) (9, 11) (b) (11, 9) (c) (3, 4) (d) (22, 18)
  39. 39.What is the distance between the points (7, 8) and (23, 20)? (a) 28 (b) 400 (c) 21 (d) 20
  40. 40.In which quadrant does the point (2, −4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant

Answer key

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

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