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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 768 · 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 midpoint of the line joining (4, 4) and (10, 16)? (a) (7, 10) (b) (10, 7) (c) (3, 6) (d) (14, 20)
  2. 2.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
  3. 3.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 6 (c) 25 (d) 7
  4. 4.In which quadrant does the point (−2, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  5. 5.In which quadrant does the point (−2, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  6. 6.What is the distance between the points (0, 16) and (8, 1)? (a) 18 (b) 23 (c) 289 (d) 17
  7. 7.What is the distance between the points (4, 2) and (16, 11)? (a) 15 (b) 21 (c) 16 (d) 225
  8. 8.What is the midpoint of the line joining (10, 2) and (12, 14)? (a) (1, 6) (b) (8, 11) (c) (11, 8) (d) (22, 16)
  9. 9.In which quadrant does the point (7, −8) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  10. 10.In which quadrant does the point (−2, 2) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  11. 11.In which quadrant does the point (7, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  12. 12.In which quadrant does the point (−1, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  13. 13.In which quadrant does the point (9, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  14. 14.What is the distance between the points (8, 5) and (11, 9)? (a) 5 (b) 7 (c) 6 (d) 25
  15. 15.In which quadrant does the point (6, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  16. 16.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  17. 17.What is the midpoint of the line joining (8, 10) and (18, 12)? (a) (13, 11) (b) (5, 1) (c) (11, 13) (d) (26, 22)
  18. 18.What is the distance between the points (4, 13) and (20, 1)? (a) 400 (b) 28 (c) 20 (d) 21
  19. 19.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  20. 20.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  21. 21.What is the midpoint of the line joining (10, 16) and (20, 4)? (a) (5, 6) (b) (30, 20) (c) (10, 15) (d) (15, 10)
  22. 22.What is the distance between the points (7, 24) and (15, 9)? (a) 23 (b) 17 (c) 289 (d) 18
  23. 23.In which quadrant does the point (6, −9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  24. 24.In which quadrant does the point (−7, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  25. 25.In which quadrant does the point (9, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  26. 26.What is the distance between the points (3, 18) and (11, 3)? (a) 23 (b) 17 (c) 18 (d) 289
  27. 27.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  28. 28.In which quadrant does the point (5, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  29. 29.What is the distance between the points (6, 11) and (14, 5)? (a) 14 (b) 100 (c) 11 (d) 10
  30. 30.What is the midpoint of the line joining (9, 3) and (13, 11)? (a) (2, 4) (b) (7, 11) (c) (22, 14) (d) (11, 7)
  31. 31.In which quadrant does the point (−2, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  32. 32.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  33. 33.What is the midpoint of the line joining (9, 14) and (17, 8)? (a) (13, 11) (b) (4, 3) (c) (26, 22) (d) (11, 13)
  34. 34.What is the distance between the points (9, 1) and (16, 25)? (a) 31 (b) 26 (c) 25 (d) 625
  35. 35.What is the distance between the points (9, 14) and (15, 6)? (a) 100 (b) 10 (c) 11 (d) 14
  36. 36.What is the distance between the points (5, 21) and (14, 9)? (a) 21 (b) 225 (c) 16 (d) 15
  37. 37.What is the midpoint of the line joining (1, 7) and (7, 5)? (a) (4, 6) (b) (6, 4) (c) (3, 1) (d) (8, 12)
  38. 38.What is the distance between the points (3, 24) and (11, 9)? (a) 289 (b) 18 (c) 23 (d) 17
  39. 39.What is the distance between the points (7, 15) and (15, 0)? (a) 17 (b) 18 (c) 23 (d) 289
  40. 40.In which quadrant does the point (−2, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant

Answer key

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

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