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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 929 · 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.In which quadrant does the point (1, −7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  2. 2.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
  3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 100 (d) 14
  4. 4.What is the distance between the points (5, 3) and (17, 8)? (a) 17 (b) 13 (c) 169 (d) 14
  5. 5.What is the distance between the points (1, 17) and (17, 5)? (a) 21 (b) 400 (c) 28 (d) 20
  6. 6.In which quadrant does the point (−1, −4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  7. 7.In which quadrant does the point (−7, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  8. 8.What is the midpoint of the line joining (1, 4) and (5, 2)? (a) (6, 6) (b) (4, 3) (c) (2, 1) (d) (3, 3)
  9. 9.What is the midpoint of the line joining (4, 8) and (10, 12)? (a) (7, 10) (b) (3, 2) (c) (14, 20) (d) (10, 7)
  10. 10.What is the distance between the points (3, 7) and (10, 31)? (a) 26 (b) 625 (c) 31 (d) 25
  11. 11.In which quadrant does the point (−2, −9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  12. 12.What is the midpoint of the line joining (8, 9) and (12, 1)? (a) (20, 10) (b) (5, 10) (c) (2, 4) (d) (10, 5)
  13. 13.What is the distance between the points (6, 6) and (12, 14)? (a) 14 (b) 100 (c) 11 (d) 10
  14. 14.What is the distance between the points (7, 6) and (13, 14)? (a) 14 (b) 11 (c) 100 (d) 10
  15. 15.What is the distance between the points (0, 20) and (9, 8)? (a) 21 (b) 15 (c) 16 (d) 225
  16. 16.What is the midpoint of the line joining (9, 8) and (19, 6)? (a) (7, 14) (b) (5, 1) (c) (28, 14) (d) (14, 7)
  17. 17.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
  18. 18.What is the distance between the points (0, 9) and (7, 33)? (a) 625 (b) 25 (c) 31 (d) 26
  19. 19.In which quadrant does the point (2, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  20. 20.What is the distance between the points (2, 18) and (11, 6)? (a) 225 (b) 16 (c) 15 (d) 21
  21. 21.What is the distance between the points (2, 3) and (14, 12)? (a) 21 (b) 15 (c) 16 (d) 225
  22. 22.What is the distance between the points (4, 1) and (12, 16)? (a) 17 (b) 23 (c) 18 (d) 289
  23. 23.In which quadrant does the point (7, 6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  24. 24.What is the midpoint of the line joining (10, 4) and (18, 10)? (a) (28, 14) (b) (4, 3) (c) (14, 7) (d) (7, 14)
  25. 25.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 13 (c) 14 (d) 17
  26. 26.In which quadrant does the point (−9, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  27. 27.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  28. 28.What is the midpoint of the line joining (3, 9) and (7, 7)? (a) (8, 5) (b) (2, 1) (c) (5, 8) (d) (10, 16)
  29. 29.What is the distance between the points (6, 15) and (14, 0)? (a) 17 (b) 18 (c) 289 (d) 23
  30. 30.What is the distance between the points (9, 9) and (15, 17)? (a) 14 (b) 100 (c) 11 (d) 10
  31. 31.What is the midpoint of the line joining (2, 16) and (8, 6)? (a) (10, 22) (b) (3, 5) (c) (11, 5) (d) (5, 11)
  32. 32.In which quadrant does the point (8, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  33. 33.What is the distance between the points (8, 9) and (20, 14)? (a) 169 (b) 13 (c) 17 (d) 14
  34. 34.In which quadrant does the point (−2, 9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  35. 35.In which quadrant does the point (2, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  36. 36.What is the midpoint of the line joining (9, 2) and (17, 14)? (a) (4, 6) (b) (8, 13) (c) (13, 8) (d) (26, 16)
  37. 37.In which quadrant does the point (3, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  38. 38.What is the distance between the points (1, 5) and (6, 17)? (a) 14 (b) 13 (c) 17 (d) 169
  39. 39.What is the distance between the points (3, 17) and (12, 5)? (a) 15 (b) 225 (c) 16 (d) 21
  40. 40.In which quadrant does the point (−9, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant

Answer key

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

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