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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 719 · 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 (1, 8) and (10, 20)? (a) 16 (b) 225 (c) 15 (d) 21
  2. 2.In which quadrant does the point (8, 6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  3. 3.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  4. 4.What is the midpoint of the line joining (2, 10) and (4, 2)? (a) (1, 4) (b) (6, 3) (c) (3, 6) (d) (6, 12)
  5. 5.What is the distance between the points (8, 3) and (14, 11)? (a) 14 (b) 100 (c) 11 (d) 10
  6. 6.In which quadrant does the point (−7, −1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  7. 7.What is the midpoint of the line joining (4, 6) and (16, 18)? (a) (6, 6) (b) (20, 24) (c) (10, 12) (d) (12, 10)
  8. 8.What is the distance between the points (7, 0) and (11, 3)? (a) 25 (b) 5 (c) 7 (d) 6
  9. 9.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
  10. 10.What is the distance between the points (1, 5) and (16, 13)? (a) 289 (b) 18 (c) 17 (d) 23
  11. 11.What is the distance between the points (9, 26) and (16, 2)? (a) 625 (b) 26 (c) 31 (d) 25
  12. 12.What is the midpoint of the line joining (1, 9) and (3, 3)? (a) (1, 3) (b) (6, 2) (c) (2, 6) (d) (4, 12)
  13. 13.What is the distance between the points (1, 19) and (6, 7)? (a) 13 (b) 17 (c) 169 (d) 14
  14. 14.What is the midpoint of the line joining (6, 8) and (18, 0)? (a) (24, 8) (b) (4, 12) (c) (6, 4) (d) (12, 4)
  15. 15.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 400 (c) 28 (d) 21
  16. 16.In which quadrant does the point (5, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  17. 17.In which quadrant does the point (−8, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  18. 18.What is the midpoint of the line joining (2, 8) and (4, 10)? (a) (9, 3) (b) (1, 1) (c) (6, 18) (d) (3, 9)
  19. 19.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 26 (d) 25
  20. 20.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  21. 21.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 18 (c) 17 (d) 23
  22. 22.In which quadrant does the point (9, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  23. 23.In which quadrant does the point (−9, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  24. 24.In which quadrant does the point (−9, −3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  25. 25.In which quadrant does the point (1, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  26. 26.What is the distance between the points (6, 26) and (13, 2)? (a) 625 (b) 31 (c) 25 (d) 26
  27. 27.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  28. 28.What is the midpoint of the line joining (8, 3) and (16, 11)? (a) (7, 12) (b) (4, 4) (c) (24, 14) (d) (12, 7)
  29. 29.What is the midpoint of the line joining (10, 14) and (22, 4)? (a) (16, 9) (b) (32, 18) (c) (9, 16) (d) (6, 5)
  30. 30.In which quadrant does the point (4, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  31. 31.What is the distance between the points (4, 1) and (7, 5)? (a) 25 (b) 5 (c) 7 (d) 6
  32. 32.What is the distance between the points (6, 15) and (21, 7)? (a) 23 (b) 289 (c) 17 (d) 18
  33. 33.What is the distance between the points (4, 3) and (16, 8)? (a) 14 (b) 169 (c) 17 (d) 13
  34. 34.What is the distance between the points (0, 8) and (12, 24)? (a) 21 (b) 20 (c) 400 (d) 28
  35. 35.In which quadrant does the point (4, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  36. 36.In which quadrant does the point (2, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  37. 37.In which quadrant does the point (−8, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  38. 38.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  39. 39.What is the distance between the points (4, 16) and (16, 7)? (a) 16 (b) 225 (c) 21 (d) 15
  40. 40.In which quadrant does the point (−2, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant

Answer key

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

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