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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 489 · 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.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  2. 2.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
  3. 3.What is the midpoint of the line joining (8, 21) and (16, 9)? (a) (12, 15) (b) (15, 12) (c) (24, 30) (d) (4, 6)
  4. 4.In which quadrant does the point (9, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  5. 5.What is the midpoint of the line joining (6, 12) and (18, 0)? (a) (6, 12) (b) (6, 6) (c) (24, 12) (d) (12, 6)
  6. 6.In which quadrant does the point (5, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  7. 7.What is the distance between the points (2, 1) and (18, 13)? (a) 21 (b) 400 (c) 20 (d) 28
  8. 8.What is the distance between the points (2, 9) and (11, 21)? (a) 16 (b) 225 (c) 21 (d) 15
  9. 9.In which quadrant does the point (−3, −1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  10. 10.What is the distance between the points (9, 29) and (16, 5)? (a) 31 (b) 25 (c) 26 (d) 625
  11. 11.What is the distance between the points (0, 2) and (8, 8)? (a) 100 (b) 11 (c) 10 (d) 14
  12. 12.What is the distance between the points (6, 5) and (9, 9)? (a) 25 (b) 6 (c) 5 (d) 7
  13. 13.What is the midpoint of the line joining (0, 9) and (2, 21)? (a) (1, 6) (b) (1, 15) (c) (2, 30) (d) (15, 1)
  14. 14.What is the distance between the points (3, 12) and (27, 5)? (a) 625 (b) 31 (c) 25 (d) 26
  15. 15.What is the distance between the points (2, 9) and (9, 33)? (a) 26 (b) 25 (c) 31 (d) 625
  16. 16.What is the distance between the points (8, 5) and (14, 13)? (a) 100 (b) 14 (c) 10 (d) 11
  17. 17.What is the distance between the points (5, 6) and (21, 18)? (a) 21 (b) 28 (c) 400 (d) 20
  18. 18.What is the midpoint of the line joining (8, 6) and (12, 10)? (a) (2, 2) (b) (10, 8) (c) (8, 10) (d) (20, 16)
  19. 19.What is the distance between the points (6, 2) and (21, 10)? (a) 23 (b) 17 (c) 289 (d) 18
  20. 20.In which quadrant does the point (1, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  21. 21.What is the distance between the points (5, 16) and (29, 9)? (a) 25 (b) 26 (c) 31 (d) 625
  22. 22.In which quadrant does the point (7, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  23. 23.What is the distance between the points (5, 31) and (12, 7)? (a) 31 (b) 625 (c) 25 (d) 26
  24. 24.What is the distance between the points (1, 5) and (6, 17)? (a) 14 (b) 17 (c) 169 (d) 13
  25. 25.What is the distance between the points (2, 8) and (17, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  26. 26.In which quadrant does the point (−5, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  27. 27.What is the distance between the points (1, 2) and (13, 7)? (a) 17 (b) 169 (c) 13 (d) 14
  28. 28.In which quadrant does the point (−3, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  29. 29.What is the distance between the points (4, 6) and (13, 18)? (a) 16 (b) 21 (c) 225 (d) 15
  30. 30.In which quadrant does the point (−9, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  31. 31.What is the distance between the points (3, 16) and (12, 4)? (a) 225 (b) 15 (c) 16 (d) 21
  32. 32.What is the midpoint of the line joining (9, 7) and (21, 15)? (a) (15, 11) (b) (30, 22) (c) (11, 15) (d) (6, 4)
  33. 33.What is the midpoint of the line joining (10, 11) and (12, 3)? (a) (22, 14) (b) (7, 11) (c) (11, 7) (d) (1, 4)
  34. 34.What is the distance between the points (2, 4) and (14, 13)? (a) 16 (b) 15 (c) 21 (d) 225
  35. 35.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  36. 36.In which quadrant does the point (−4, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  37. 37.In which quadrant does the point (−8, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  38. 38.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
  39. 39.In which quadrant does the point (8, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  40. 40.In which quadrant does the point (−3, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant

Answer key

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

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