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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 239 · 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 distance between the points (4, 4) and (11, 28)? (a) 31 (b) 625 (c) 26 (d) 25
  2. 2.In which quadrant does the point (5, 4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  3. 3.In which quadrant does the point (1, 7) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  4. 4.What is the distance between the points (1, 8) and (9, 14)? (a) 10 (b) 100 (c) 14 (d) 11
  5. 5.What is the midpoint of the line joining (8, 11) and (10, 5)? (a) (18, 16) (b) (9, 8) (c) (1, 3) (d) (8, 9)
  6. 6.What is the midpoint of the line joining (0, 1) and (4, 11)? (a) (2, 6) (b) (4, 12) (c) (2, 5) (d) (6, 2)
  7. 7.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  8. 8.What is the midpoint of the line joining (7, 3) and (13, 7)? (a) (5, 10) (b) (20, 10) (c) (3, 2) (d) (10, 5)
  9. 9.In which quadrant does the point (7, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  10. 10.What is the distance between the points (9, 8) and (21, 17)? (a) 21 (b) 225 (c) 15 (d) 16
  11. 11.What is the midpoint of the line joining (5, 6) and (17, 0)? (a) (11, 3) (b) (6, 3) (c) (3, 11) (d) (22, 6)
  12. 12.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
  13. 13.In which quadrant does the point (3, 7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  14. 14.What is the distance between the points (2, 0) and (5, 4)? (a) 25 (b) 7 (c) 6 (d) 5
  15. 15.What is the distance between the points (1, 9) and (16, 1)? (a) 17 (b) 18 (c) 289 (d) 23
  16. 16.In which quadrant does the point (−7, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  17. 17.In which quadrant does the point (−6, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  18. 18.In which quadrant does the point (−1, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  19. 19.What is the distance between the points (2, 16) and (17, 8)? (a) 18 (b) 17 (c) 23 (d) 289
  20. 20.What is the distance between the points (2, 12) and (11, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  21. 21.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 15 (c) 225 (d) 16
  22. 22.What is the distance between the points (2, 8) and (17, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  23. 23.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  24. 24.What is the distance between the points (8, 3) and (14, 11)? (a) 11 (b) 14 (c) 100 (d) 10
  25. 25.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  26. 26.What is the midpoint of the line joining (4, 4) and (6, 14)? (a) (1, 5) (b) (9, 5) (c) (5, 9) (d) (10, 18)
  27. 27.In which quadrant does the point (6, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  28. 28.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 21 (d) 400
  29. 29.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  30. 30.In which quadrant does the point (3, −4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  31. 31.What is the distance between the points (3, 14) and (8, 2)? (a) 14 (b) 169 (c) 13 (d) 17
  32. 32.What is the midpoint of the line joining (6, 11) and (18, 7)? (a) (6, 2) (b) (24, 18) (c) (12, 9) (d) (9, 12)
  33. 33.What is the midpoint of the line joining (0, 1) and (4, 9)? (a) (2, 5) (b) (5, 2) (c) (4, 10) (d) (2, 4)
  34. 34.What is the midpoint of the line joining (7, 0) and (9, 10)? (a) (16, 10) (b) (1, 5) (c) (5, 8) (d) (8, 5)
  35. 35.In which quadrant does the point (5, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  36. 36.What is the distance between the points (8, 12) and (12, 9)? (a) 25 (b) 7 (c) 5 (d) 6
  37. 37.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 225 (d) 21
  38. 38.In which quadrant does the point (3, 2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  39. 39.In which quadrant does the point (−1, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.What is the midpoint of the line joining (4, 11) and (6, 3)? (a) (1, 4) (b) (7, 5) (c) (10, 14) (d) (5, 7)

Answer key

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

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