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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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