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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 844 · 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 (2, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  2. 2.In which quadrant does the point (−3, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  3. 3.What is the midpoint of the line joining (0, 2) and (6, 6)? (a) (3, 2) (b) (3, 4) (c) (6, 8) (d) (4, 3)
  4. 4.What is the distance between the points (3, 8) and (7, 11)? (a) 5 (b) 25 (c) 7 (d) 6
  5. 5.What is the midpoint of the line joining (4, 8) and (6, 12)? (a) (5, 10) (b) (10, 20) (c) (10, 5) (d) (1, 2)
  6. 6.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  7. 7.What is the midpoint of the line joining (5, 2) and (7, 6)? (a) (1, 2) (b) (6, 4) (c) (4, 6) (d) (12, 8)
  8. 8.What is the midpoint of the line joining (8, 8) and (14, 2)? (a) (3, 3) (b) (5, 11) (c) (22, 10) (d) (11, 5)
  9. 9.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  10. 10.What is the distance between the points (9, 9) and (24, 17)? (a) 289 (b) 23 (c) 18 (d) 17
  11. 11.What is the distance between the points (2, 33) and (9, 9)? (a) 31 (b) 26 (c) 625 (d) 25
  12. 12.What is the distance between the points (4, 7) and (16, 12)? (a) 17 (b) 14 (c) 169 (d) 13
  13. 13.In which quadrant does the point (−3, −2) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  14. 14.In which quadrant does the point (−6, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  15. 15.In which quadrant does the point (7, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  16. 16.What is the midpoint of the line joining (3, 0) and (15, 8)? (a) (4, 9) (b) (6, 4) (c) (18, 8) (d) (9, 4)
  17. 17.What is the midpoint of the line joining (1, 8) and (11, 6)? (a) (6, 7) (b) (7, 6) (c) (12, 14) (d) (5, 1)
  18. 18.What is the distance between the points (7, 12) and (13, 4)? (a) 100 (b) 14 (c) 11 (d) 10
  19. 19.What is the distance between the points (9, 7) and (12, 11)? (a) 6 (b) 7 (c) 5 (d) 25
  20. 20.In which quadrant does the point (3, 3) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  21. 21.In which quadrant does the point (−1, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  22. 22.In which quadrant does the point (−7, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  23. 23.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  24. 24.What is the distance between the points (6, 8) and (13, 32)? (a) 25 (b) 31 (c) 26 (d) 625
  25. 25.What is the distance between the points (8, 17) and (23, 9)? (a) 17 (b) 18 (c) 289 (d) 23
  26. 26.What is the distance between the points (1, 12) and (25, 5)? (a) 31 (b) 26 (c) 625 (d) 25
  27. 27.What is the midpoint of the line joining (1, 12) and (5, 8)? (a) (2, 2) (b) (6, 20) (c) (10, 3) (d) (3, 10)
  28. 28.What is the distance between the points (2, 9) and (8, 1)? (a) 14 (b) 11 (c) 10 (d) 100
  29. 29.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 25 (c) 625 (d) 26
  30. 30.What is the midpoint of the line joining (8, 12) and (18, 4)? (a) (8, 13) (b) (26, 16) (c) (13, 8) (d) (5, 4)
  31. 31.In which quadrant does the point (6, 4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  32. 32.In which quadrant does the point (−7, 9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  33. 33.What is the distance between the points (7, 0) and (13, 8)? (a) 14 (b) 11 (c) 10 (d) 100
  34. 34.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 169 (d) 17
  35. 35.What is the distance between the points (3, 14) and (18, 6)? (a) 18 (b) 17 (c) 23 (d) 289
  36. 36.What is the midpoint of the line joining (7, 7) and (11, 1)? (a) (4, 9) (b) (18, 8) (c) (9, 4) (d) (2, 3)
  37. 37.What is the midpoint of the line joining (8, 3) and (18, 9)? (a) (6, 13) (b) (26, 12) (c) (5, 3) (d) (13, 6)
  38. 38.What is the distance between the points (3, 9) and (15, 25)? (a) 21 (b) 400 (c) 28 (d) 20
  39. 39.What is the distance between the points (9, 33) and (16, 9)? (a) 31 (b) 26 (c) 25 (d) 625
  40. 40.What is the midpoint of the line joining (9, 2) and (19, 4)? (a) (3, 14) (b) (28, 6) (c) (14, 3) (d) (5, 1)

Answer key

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

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