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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 432 · 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 midpoint of the line joining (5, 3) and (15, 13)? (a) (20, 16) (b) (5, 5) (c) (8, 10) (d) (10, 8)
  2. 2.What is the distance between the points (4, 2) and (11, 26)? (a) 625 (b) 25 (c) 26 (d) 31
  3. 3.What is the midpoint of the line joining (9, 4) and (13, 8)? (a) (6, 11) (b) (11, 6) (c) (22, 12) (d) (2, 2)
  4. 4.In which quadrant does the point (−9, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  5. 5.In which quadrant does the point (−9, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  6. 6.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 625 (c) 31 (d) 26
  7. 7.What is the midpoint of the line joining (10, 3) and (16, 7)? (a) (5, 13) (b) (26, 10) (c) (13, 5) (d) (3, 2)
  8. 8.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 21 (d) 225
  9. 9.What is the distance between the points (7, 14) and (19, 9)? (a) 14 (b) 17 (c) 169 (d) 13
  10. 10.What is the distance between the points (9, 19) and (21, 3)? (a) 20 (b) 28 (c) 21 (d) 400
  11. 11.What is the distance between the points (9, 7) and (13, 10)? (a) 7 (b) 6 (c) 5 (d) 25
  12. 12.In which quadrant does the point (3, −8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  13. 13.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  14. 14.What is the midpoint of the line joining (1, 12) and (9, 0)? (a) (10, 12) (b) (4, 6) (c) (5, 6) (d) (6, 5)
  15. 15.In which quadrant does the point (−2, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  16. 16.In which quadrant does the point (−1, −6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  17. 17.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  18. 18.What is the midpoint of the line joining (5, 8) and (9, 12)? (a) (10, 7) (b) (2, 2) (c) (7, 10) (d) (14, 20)
  19. 19.In which quadrant does the point (2, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  20. 20.In which quadrant does the point (8, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  21. 21.In which quadrant does the point (−3, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  22. 22.What is the midpoint of the line joining (0, 16) and (2, 6)? (a) (2, 22) (b) (1, 5) (c) (11, 1) (d) (1, 11)
  23. 23.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  24. 24.What is the distance between the points (1, 2) and (25, 9)? (a) 26 (b) 625 (c) 31 (d) 25
  25. 25.What is the distance between the points (0, 10) and (12, 1)? (a) 21 (b) 225 (c) 15 (d) 16
  26. 26.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  27. 27.What is the midpoint of the line joining (0, 3) and (12, 9)? (a) (7, 6) (b) (12, 12) (c) (6, 6) (d) (6, 3)
  28. 28.What is the distance between the points (2, 3) and (8, 11)? (a) 11 (b) 100 (c) 10 (d) 14
  29. 29.In which quadrant does the point (−7, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  30. 30.In which quadrant does the point (9, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  31. 31.In which quadrant does the point (−5, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  32. 32.What is the distance between the points (1, 14) and (6, 2)? (a) 13 (b) 17 (c) 14 (d) 169
  33. 33.In which quadrant does the point (8, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  34. 34.In which quadrant does the point (−9, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  35. 35.In which quadrant does the point (9, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  36. 36.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  37. 37.What is the distance between the points (6, 0) and (10, 3)? (a) 6 (b) 7 (c) 25 (d) 5
  38. 38.What is the distance between the points (0, 5) and (24, 12)? (a) 26 (b) 625 (c) 25 (d) 31
  39. 39.In which quadrant does the point (−3, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  40. 40.What is the distance between the points (2, 7) and (7, 19)? (a) 17 (b) 14 (c) 13 (d) 169

Answer key

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

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