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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 383 · 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 (7, 5) and (15, 20)? (a) 23 (b) 17 (c) 18 (d) 289
  2. 2.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  3. 3.In which quadrant does the point (9, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  4. 4.In which quadrant does the point (−1, 4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  5. 5.What is the midpoint of the line joining (2, 18) and (10, 10)? (a) (12, 28) (b) (14, 6) (c) (6, 14) (d) (4, 4)
  6. 6.What is the distance between the points (6, 9) and (18, 4)? (a) 14 (b) 17 (c) 13 (d) 169
  7. 7.In which quadrant does the point (−4, 2) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  8. 8.What is the distance between the points (2, 3) and (6, 6)? (a) 5 (b) 25 (c) 7 (d) 6
  9. 9.In which quadrant does the point (6, −1) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  10. 10.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  11. 11.In which quadrant does the point (−6, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  12. 12.What is the midpoint of the line joining (6, 2) and (16, 4)? (a) (22, 6) (b) (3, 11) (c) (5, 1) (d) (11, 3)
  13. 13.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
  14. 14.In which quadrant does the point (−8, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  15. 15.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  16. 16.In which quadrant does the point (−8, −9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third 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.What is the distance between the points (7, 6) and (11, 3)? (a) 25 (b) 5 (c) 6 (d) 7
  19. 19.What is the midpoint of the line joining (7, 8) and (13, 16)? (a) (10, 12) (b) (12, 10) (c) (20, 24) (d) (3, 4)
  20. 20.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  21. 21.What is the midpoint of the line joining (4, 0) and (16, 12)? (a) (20, 12) (b) (6, 6) (c) (10, 6) (d) (6, 10)
  22. 22.In which quadrant does the point (3, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  23. 23.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 21 (c) 15 (d) 225
  24. 24.What is the midpoint of the line joining (4, 18) and (16, 10)? (a) (20, 28) (b) (10, 14) (c) (14, 10) (d) (6, 4)
  25. 25.What is the distance between the points (6, 9) and (10, 6)? (a) 5 (b) 6 (c) 25 (d) 7
  26. 26.In which quadrant does the point (5, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  27. 27.What is the distance between the points (6, 13) and (18, 4)? (a) 15 (b) 16 (c) 21 (d) 225
  28. 28.In which quadrant does the point (−6, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  29. 29.What is the distance between the points (5, 15) and (13, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  30. 30.What is the distance between the points (2, 4) and (9, 28)? (a) 25 (b) 31 (c) 625 (d) 26
  31. 31.In which quadrant does the point (7, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  32. 32.In which quadrant does the point (−1, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  33. 33.What is the midpoint of the line joining (3, 8) and (5, 14)? (a) (11, 4) (b) (1, 3) (c) (8, 22) (d) (4, 11)
  34. 34.What is the distance between the points (9, 2) and (16, 26)? (a) 25 (b) 625 (c) 26 (d) 31
  35. 35.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  36. 36.What is the distance between the points (8, 2) and (14, 10)? (a) 11 (b) 100 (c) 10 (d) 14
  37. 37.What is the distance between the points (1, 9) and (13, 25)? (a) 400 (b) 20 (c) 28 (d) 21
  38. 38.What is the distance between the points (7, 9) and (22, 17)? (a) 17 (b) 23 (c) 289 (d) 18
  39. 39.In which quadrant does the point (−5, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  40. 40.What is the distance between the points (4, 4) and (12, 19)? (a) 23 (b) 17 (c) 289 (d) 18

Answer key

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

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