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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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