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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 916 · 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.In which quadrant does the point (8, −7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  2. 2.What is the distance between the points (9, 6) and (16, 30)? (a) 26 (b) 625 (c) 31 (d) 25
  3. 3.What is the distance between the points (1, 1) and (8, 25)? (a) 26 (b) 25 (c) 625 (d) 31
  4. 4.What is the distance between the points (3, 11) and (9, 3)? (a) 14 (b) 11 (c) 100 (d) 10
  5. 5.What is the midpoint of the line joining (6, 3) and (10, 5)? (a) (2, 1) (b) (16, 8) (c) (4, 8) (d) (8, 4)
  6. 6.In which quadrant does the point (−7, −2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  7. 7.In which quadrant does the point (−5, 4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  8. 8.What is the midpoint of the line joining (1, 2) and (5, 8)? (a) (5, 3) (b) (2, 3) (c) (6, 10) (d) (3, 5)
  9. 9.What is the midpoint of the line joining (1, 8) and (9, 6)? (a) (4, 1) (b) (10, 14) (c) (5, 7) (d) (7, 5)
  10. 10.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  11. 11.What is the distance between the points (1, 9) and (5, 12)? (a) 6 (b) 7 (c) 25 (d) 5
  12. 12.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 21 (c) 225 (d) 16
  13. 13.What is the midpoint of the line joining (4, 6) and (14, 2)? (a) (18, 8) (b) (9, 4) (c) (4, 9) (d) (5, 2)
  14. 14.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  15. 15.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
  16. 16.What is the midpoint of the line joining (4, 4) and (16, 8)? (a) (6, 10) (b) (20, 12) (c) (6, 2) (d) (10, 6)
  17. 17.What is the midpoint of the line joining (2, 7) and (10, 9)? (a) (6, 8) (b) (8, 6) (c) (4, 1) (d) (12, 16)
  18. 18.What is the distance between the points (5, 16) and (14, 4)? (a) 16 (b) 21 (c) 15 (d) 225
  19. 19.In which quadrant does the point (−1, 7) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  20. 20.What is the midpoint of the line joining (1, 13) and (3, 3)? (a) (4, 16) (b) (8, 2) (c) (2, 8) (d) (1, 5)
  21. 21.In which quadrant does the point (−6, −7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  22. 22.What is the distance between the points (2, 4) and (14, 13)? (a) 225 (b) 15 (c) 21 (d) 16
  23. 23.What is the midpoint of the line joining (6, 18) and (10, 6)? (a) (12, 8) (b) (2, 6) (c) (8, 12) (d) (16, 24)
  24. 24.What is the distance between the points (9, 8) and (16, 32)? (a) 26 (b) 25 (c) 31 (d) 625
  25. 25.What is the distance between the points (8, 12) and (12, 9)? (a) 7 (b) 6 (c) 25 (d) 5
  26. 26.What is the distance between the points (1, 3) and (4, 7)? (a) 5 (b) 6 (c) 25 (d) 7
  27. 27.In which quadrant does the point (6, −5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  28. 28.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  29. 29.What is the distance between the points (2, 0) and (6, 3)? (a) 6 (b) 7 (c) 25 (d) 5
  30. 30.What is the midpoint of the line joining (2, 0) and (14, 10)? (a) (8, 5) (b) (5, 8) (c) (6, 5) (d) (16, 10)
  31. 31.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 225 (d) 15
  32. 32.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  33. 33.What is the distance between the points (0, 22) and (12, 6)? (a) 400 (b) 28 (c) 20 (d) 21
  34. 34.In which quadrant does the point (9, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  35. 35.What is the distance between the points (2, 4) and (11, 16)? (a) 16 (b) 225 (c) 21 (d) 15
  36. 36.What is the midpoint of the line joining (2, 18) and (14, 6)? (a) (6, 6) (b) (12, 8) (c) (16, 24) (d) (8, 12)
  37. 37.What is the distance between the points (2, 16) and (17, 8)? (a) 23 (b) 17 (c) 18 (d) 289
  38. 38.What is the distance between the points (6, 6) and (14, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  39. 39.What is the distance between the points (1, 1) and (9, 7)? (a) 14 (b) 11 (c) 100 (d) 10
  40. 40.In which quadrant does the point (−4, −1) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant

Answer key

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

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