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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 762 · 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 (−2, −2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  2. 2.What is the distance between the points (6, 5) and (13, 29)? (a) 625 (b) 31 (c) 26 (d) 25
  3. 3.In which quadrant does the point (8, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  4. 4.What is the midpoint of the line joining (1, 10) and (9, 20)? (a) (10, 30) (b) (5, 15) (c) (4, 5) (d) (15, 5)
  5. 5.In which quadrant does the point (6, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  6. 6.What is the midpoint of the line joining (2, 5) and (4, 13)? (a) (1, 4) (b) (9, 3) (c) (3, 9) (d) (6, 18)
  7. 7.What is the distance between the points (5, 8) and (13, 14)? (a) 14 (b) 11 (c) 10 (d) 100
  8. 8.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  9. 9.What is the midpoint of the line joining (3, 7) and (9, 1)? (a) (4, 6) (b) (6, 4) (c) (12, 8) (d) (3, 3)
  10. 10.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  11. 11.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  12. 12.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 289 (d) 23
  13. 13.What is the distance between the points (7, 0) and (16, 12)? (a) 225 (b) 21 (c) 16 (d) 15
  14. 14.What is the distance between the points (1, 8) and (7, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  15. 15.In which quadrant does the point (9, −3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  16. 16.What is the midpoint of the line joining (10, 15) and (14, 7)? (a) (24, 22) (b) (12, 11) (c) (2, 4) (d) (11, 12)
  17. 17.In which quadrant does the point (1, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  18. 18.In which quadrant does the point (−7, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  19. 19.In which quadrant does the point (−8, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  20. 20.How far is the point (24, 7) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
  21. 21.In which quadrant does the point (−6, 2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  22. 22.In which quadrant does the point (7, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  23. 23.In which quadrant does the point (−2, −4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  24. 24.In which quadrant does the point (−6, −5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  25. 25.What is the distance between the points (6, 1) and (12, 9)? (a) 14 (b) 10 (c) 11 (d) 100
  26. 26.What is the distance between the points (3, 10) and (18, 2)? (a) 23 (b) 17 (c) 289 (d) 18
  27. 27.What is the distance between the points (0, 21) and (9, 9)? (a) 15 (b) 225 (c) 16 (d) 21
  28. 28.What is the midpoint of the line joining (6, 15) and (16, 7)? (a) (5, 4) (b) (11, 11) (c) (22, 22) (d) (12, 11)
  29. 29.What is the distance between the points (7, 24) and (19, 8)? (a) 21 (b) 400 (c) 20 (d) 28
  30. 30.What is the distance between the points (0, 5) and (3, 1)? (a) 7 (b) 25 (c) 5 (d) 6
  31. 31.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  32. 32.In which quadrant does the point (1, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  33. 33.In which quadrant does the point (−1, 2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  34. 34.What is the distance between the points (8, 9) and (14, 1)? (a) 10 (b) 11 (c) 100 (d) 14
  35. 35.In which quadrant does the point (5, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  36. 36.In which quadrant does the point (3, 6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  37. 37.What is the distance between the points (9, 8) and (12, 4)? (a) 7 (b) 6 (c) 5 (d) 25
  38. 38.What is the distance between the points (2, 1) and (26, 8)? (a) 25 (b) 625 (c) 26 (d) 31
  39. 39.In which quadrant does the point (8, 4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  40. 40.What is the midpoint of the line joining (9, 0) and (15, 2)? (a) (24, 2) (b) (12, 1) (c) (3, 1) (d) (1, 12)

Answer key

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

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