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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 649 · 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 (1, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  2. 2.What is the distance between the points (9, 13) and (17, 7)? (a) 100 (b) 14 (c) 10 (d) 11
  3. 3.In which quadrant does the point (1, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  4. 4.In which quadrant does the point (−7, −9) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  5. 5.What is the distance between the points (6, 4) and (21, 12)? (a) 23 (b) 289 (c) 18 (d) 17
  6. 6.What is the distance between the points (7, 10) and (19, 5)? (a) 169 (b) 13 (c) 17 (d) 14
  7. 7.What is the midpoint of the line joining (4, 4) and (6, 10)? (a) (5, 7) (b) (10, 14) (c) (7, 5) (d) (1, 3)
  8. 8.What is the midpoint of the line joining (3, 1) and (7, 11)? (a) (2, 5) (b) (10, 12) (c) (6, 5) (d) (5, 6)
  9. 9.What is the distance between the points (1, 6) and (17, 18)? (a) 28 (b) 400 (c) 21 (d) 20
  10. 10.How far is the point (12, 16) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  11. 11.What is the midpoint of the line joining (1, 13) and (3, 1)? (a) (1, 6) (b) (4, 14) (c) (2, 7) (d) (7, 2)
  12. 12.What is the midpoint of the line joining (6, 2) and (8, 14)? (a) (1, 6) (b) (8, 7) (c) (14, 16) (d) (7, 8)
  13. 13.What is the midpoint of the line joining (10, 5) and (16, 7)? (a) (3, 1) (b) (26, 12) (c) (13, 6) (d) (6, 13)
  14. 14.What is the distance between the points (2, 7) and (14, 16)? (a) 225 (b) 21 (c) 15 (d) 16
  15. 15.What is the distance between the points (2, 1) and (5, 5)? (a) 6 (b) 5 (c) 25 (d) 7
  16. 16.What is the distance between the points (7, 1) and (13, 9)? (a) 10 (b) 11 (c) 100 (d) 14
  17. 17.What is the midpoint of the line joining (2, 10) and (4, 22)? (a) (1, 6) (b) (6, 32) (c) (16, 3) (d) (3, 16)
  18. 18.What is the distance between the points (6, 14) and (21, 6)? (a) 18 (b) 289 (c) 17 (d) 23
  19. 19.In which quadrant does the point (−7, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  20. 20.In which quadrant does the point (8, −3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  21. 21.What is the distance between the points (2, 4) and (6, 1)? (a) 25 (b) 5 (c) 7 (d) 6
  22. 22.What is the distance between the points (4, 12) and (13, 0)? (a) 225 (b) 21 (c) 15 (d) 16
  23. 23.What is the midpoint of the line joining (0, 12) and (2, 2)? (a) (1, 5) (b) (7, 1) (c) (1, 7) (d) (2, 14)
  24. 24.What is the distance between the points (6, 15) and (11, 3)? (a) 13 (b) 17 (c) 169 (d) 14
  25. 25.What is the midpoint of the line joining (10, 13) and (18, 5)? (a) (4, 4) (b) (14, 9) (c) (28, 18) (d) (9, 14)
  26. 26.In which quadrant does the point (−3, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  27. 27.What is the distance between the points (8, 15) and (14, 7)? (a) 10 (b) 14 (c) 11 (d) 100
  28. 28.In which quadrant does the point (5, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  29. 29.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 31 (d) 625
  30. 30.What is the midpoint of the line joining (5, 10) and (7, 4)? (a) (6, 7) (b) (7, 6) (c) (12, 14) (d) (1, 3)
  31. 31.In which quadrant does the point (7, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  32. 32.In which quadrant does the point (−6, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  33. 33.What is the midpoint of the line joining (2, 5) and (10, 7)? (a) (12, 12) (b) (4, 1) (c) (7, 6) (d) (6, 6)
  34. 34.In which quadrant does the point (8, 2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  35. 35.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  36. 36.What is the midpoint of the line joining (2, 12) and (10, 0)? (a) (4, 6) (b) (12, 12) (c) (7, 6) (d) (6, 6)
  37. 37.In which quadrant does the point (1, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  38. 38.What is the distance between the points (7, 12) and (12, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  39. 39.What is the midpoint of the line joining (6, 12) and (18, 0)? (a) (6, 12) (b) (6, 6) (c) (12, 6) (d) (24, 12)
  40. 40.In which quadrant does the point (2, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant

Answer key

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

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