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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 714 · 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 (6, 16) and (12, 8)? (a) 14 (b) 100 (c) 11 (d) 10
  2. 2.What is the distance between the points (6, 5) and (18, 10)? (a) 13 (b) 14 (c) 17 (d) 169
  3. 3.What is the distance between the points (9, 5) and (17, 11)? (a) 10 (b) 100 (c) 14 (d) 11
  4. 4.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 13 (c) 169 (d) 14
  5. 5.In which quadrant does the point (4, −2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  6. 6.What is the midpoint of the line joining (8, 3) and (10, 9)? (a) (6, 9) (b) (18, 12) (c) (1, 3) (d) (9, 6)
  7. 7.In which quadrant does the point (9, 7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  8. 8.In which quadrant does the point (8, −3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  9. 9.In which quadrant does the point (3, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  10. 10.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  11. 11.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  12. 12.In which quadrant does the point (1, −7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  13. 13.In which quadrant does the point (4, 6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  14. 14.In which quadrant does the point (1, 9) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  15. 15.What is the distance between the points (6, 24) and (14, 9)? (a) 17 (b) 23 (c) 289 (d) 18
  16. 16.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  17. 17.What is the midpoint of the line joining (4, 9) and (6, 19)? (a) (5, 14) (b) (14, 5) (c) (10, 28) (d) (1, 5)
  18. 18.What is the distance between the points (4, 12) and (16, 3)? (a) 16 (b) 21 (c) 15 (d) 225
  19. 19.What is the distance between the points (9, 7) and (18, 19)? (a) 21 (b) 15 (c) 225 (d) 16
  20. 20.What is the midpoint of the line joining (4, 17) and (14, 9)? (a) (18, 26) (b) (5, 4) (c) (13, 9) (d) (9, 13)
  21. 21.What is the distance between the points (7, 5) and (22, 13)? (a) 18 (b) 23 (c) 17 (d) 289
  22. 22.In which quadrant does the point (3, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  23. 23.In which quadrant does the point (−2, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  24. 24.In which quadrant does the point (2, 6) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  25. 25.What is the distance between the points (4, 9) and (11, 33)? (a) 31 (b) 26 (c) 25 (d) 625
  26. 26.In which quadrant does the point (−4, 1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  27. 27.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  28. 28.What is the midpoint of the line joining (6, 9) and (14, 15)? (a) (12, 10) (b) (20, 24) (c) (4, 3) (d) (10, 12)
  29. 29.What is the midpoint of the line joining (4, 8) and (14, 6)? (a) (5, 1) (b) (18, 14) (c) (9, 7) (d) (7, 9)
  30. 30.What is the distance between the points (5, 20) and (21, 8)? (a) 400 (b) 28 (c) 21 (d) 20
  31. 31.In which quadrant does the point (9, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  32. 32.What is the midpoint of the line joining (3, 7) and (7, 11)? (a) (9, 5) (b) (2, 2) (c) (10, 18) (d) (5, 9)
  33. 33.What is the distance between the points (5, 7) and (13, 22)? (a) 17 (b) 289 (c) 18 (d) 23
  34. 34.What is the midpoint of the line joining (8, 4) and (16, 12)? (a) (8, 12) (b) (12, 8) (c) (24, 16) (d) (4, 4)
  35. 35.In which quadrant does the point (−8, 1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  36. 36.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  37. 37.What is the distance between the points (5, 12) and (9, 9)? (a) 6 (b) 25 (c) 7 (d) 5
  38. 38.In which quadrant does the point (−2, −2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  39. 39.What is the midpoint of the line joining (1, 13) and (3, 5)? (a) (9, 2) (b) (4, 18) (c) (1, 4) (d) (2, 9)
  40. 40.What is the distance between the points (5, 7) and (29, 0)? (a) 31 (b) 25 (c) 625 (d) 26

Answer key

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

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