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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 574 · 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, 6) and (7, 14)? (a) 10 (b) 14 (c) 100 (d) 11
  2. 2.In which quadrant does the point (−6, −1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  3. 3.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  4. 4.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  5. 5.In which quadrant does the point (−7, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  6. 6.In which quadrant does the point (9, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  7. 7.What is the midpoint of the line joining (7, 8) and (19, 18)? (a) (14, 13) (b) (26, 26) (c) (6, 5) (d) (13, 13)
  8. 8.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  9. 9.What is the distance between the points (6, 11) and (18, 6)? (a) 17 (b) 14 (c) 13 (d) 169
  10. 10.What is the distance between the points (0, 9) and (8, 3)? (a) 14 (b) 10 (c) 11 (d) 100
  11. 11.What is the midpoint of the line joining (10, 9) and (16, 15)? (a) (26, 24) (b) (13, 12) (c) (3, 3) (d) (12, 13)
  12. 12.What is the distance between the points (5, 9) and (20, 17)? (a) 23 (b) 18 (c) 17 (d) 289
  13. 13.In which quadrant does the point (−5, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  14. 14.What is the distance between the points (8, 7) and (11, 11)? (a) 7 (b) 25 (c) 6 (d) 5
  15. 15.What is the midpoint of the line joining (0, 10) and (12, 4)? (a) (7, 6) (b) (6, 7) (c) (6, 3) (d) (12, 14)
  16. 16.What is the midpoint of the line joining (4, 10) and (10, 2)? (a) (14, 12) (b) (3, 4) (c) (7, 6) (d) (6, 7)
  17. 17.What is the distance between the points (5, 7) and (9, 10)? (a) 6 (b) 25 (c) 5 (d) 7
  18. 18.What is the distance between the points (1, 7) and (7, 15)? (a) 14 (b) 10 (c) 100 (d) 11
  19. 19.What is the distance between the points (3, 0) and (15, 9)? (a) 15 (b) 16 (c) 21 (d) 225
  20. 20.What is the distance between the points (4, 8) and (28, 1)? (a) 31 (b) 625 (c) 26 (d) 25
  21. 21.What is the distance between the points (1, 3) and (5, 0)? (a) 5 (b) 6 (c) 7 (d) 25
  22. 22.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 14 (d) 169
  23. 23.What is the distance between the points (9, 2) and (21, 7)? (a) 17 (b) 14 (c) 169 (d) 13
  24. 24.In which quadrant does the point (−3, 3) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  25. 25.In which quadrant does the point (8, 3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  26. 26.What is the distance between the points (2, 23) and (10, 8)? (a) 289 (b) 18 (c) 23 (d) 17
  27. 27.What is the distance between the points (7, 11) and (13, 3)? (a) 10 (b) 14 (c) 100 (d) 11
  28. 28.In which quadrant does the point (7, 4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  29. 29.What is the distance between the points (2, 5) and (5, 1)? (a) 6 (b) 25 (c) 7 (d) 5
  30. 30.What is the distance between the points (7, 5) and (23, 17)? (a) 20 (b) 400 (c) 28 (d) 21
  31. 31.In which quadrant does the point (6, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  32. 32.In which quadrant does the point (8, 8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  33. 33.What is the distance between the points (2, 13) and (14, 4)? (a) 21 (b) 16 (c) 15 (d) 225
  34. 34.What is the distance between the points (3, 9) and (10, 33)? (a) 31 (b) 625 (c) 26 (d) 25
  35. 35.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  36. 36.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  37. 37.In which quadrant does the point (7, 8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  38. 38.In which quadrant does the point (8, −2) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  39. 39.What is the midpoint of the line joining (0, 5) and (10, 17)? (a) (11, 5) (b) (10, 22) (c) (5, 11) (d) (5, 6)
  40. 40.What is the midpoint of the line joining (9, 6) and (11, 12)? (a) (20, 18) (b) (1, 3) (c) (9, 10) (d) (10, 9)

Answer key

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

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