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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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