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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 872 · 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 (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  2. 2.In which quadrant does the point (−9, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  3. 3.What is the distance between the points (8, 5) and (12, 2)? (a) 7 (b) 25 (c) 6 (d) 5
  4. 4.In which quadrant does the point (−3, 8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  5. 5.What is the distance between the points (8, 15) and (17, 3)? (a) 16 (b) 15 (c) 21 (d) 225
  6. 6.What is the distance between the points (2, 11) and (8, 3)? (a) 100 (b) 11 (c) 10 (d) 14
  7. 7.In which quadrant does the point (−1, 5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  8. 8.In which quadrant does the point (−8, −4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  9. 9.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  10. 10.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
  11. 11.In which quadrant does the point (−5, −5) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  12. 12.In which quadrant does the point (−4, −5) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  13. 13.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 18 (c) 23 (d) 289
  14. 14.What is the distance between the points (6, 6) and (14, 12)? (a) 100 (b) 14 (c) 11 (d) 10
  15. 15.In which quadrant does the point (9, 7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  16. 16.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 7 (c) 25 (d) 5
  17. 17.In which quadrant does the point (3, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  18. 18.What is the distance between the points (3, 4) and (15, 9)? (a) 14 (b) 13 (c) 169 (d) 17
  19. 19.In which quadrant does the point (−2, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  20. 20.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
  21. 21.What is the midpoint of the line joining (3, 2) and (15, 0)? (a) (18, 2) (b) (1, 9) (c) (9, 1) (d) (6, 1)
  22. 22.What is the distance between the points (3, 23) and (11, 8)? (a) 17 (b) 23 (c) 289 (d) 18
  23. 23.What is the distance between the points (9, 23) and (17, 8)? (a) 17 (b) 289 (c) 23 (d) 18
  24. 24.What is the midpoint of the line joining (3, 7) and (11, 13)? (a) (14, 20) (b) (7, 10) (c) (4, 3) (d) (10, 7)
  25. 25.What is the distance between the points (2, 20) and (14, 4)? (a) 20 (b) 21 (c) 28 (d) 400
  26. 26.In which quadrant does the point (−5, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  27. 27.What is the distance between the points (2, 33) and (9, 9)? (a) 25 (b) 625 (c) 31 (d) 26
  28. 28.In which quadrant does the point (−7, 6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  29. 29.What is the distance between the points (6, 8) and (15, 20)? (a) 15 (b) 21 (c) 225 (d) 16
  30. 30.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  31. 31.What is the midpoint of the line joining (3, 4) and (5, 0)? (a) (2, 4) (b) (1, 2) (c) (8, 4) (d) (4, 2)
  32. 32.What is the distance between the points (8, 5) and (20, 14)? (a) 21 (b) 16 (c) 15 (d) 225
  33. 33.What is the midpoint of the line joining (4, 5) and (14, 17)? (a) (18, 22) (b) (5, 6) (c) (9, 11) (d) (11, 9)
  34. 34.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 14 (c) 11 (d) 100
  35. 35.What is the distance between the points (8, 7) and (16, 1)? (a) 100 (b) 14 (c) 10 (d) 11
  36. 36.In which quadrant does the point (−1, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  37. 37.In which quadrant does the point (−6, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  38. 38.What is the distance between the points (8, 3) and (11, 7)? (a) 5 (b) 25 (c) 7 (d) 6
  39. 39.What is the midpoint of the line joining (7, 4) and (9, 0)? (a) (16, 4) (b) (8, 2) (c) (2, 8) (d) (1, 2)
  40. 40.What is the distance between the points (4, 0) and (11, 24)? (a) 625 (b) 26 (c) 31 (d) 25

Answer key

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

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