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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 49 · 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 (3, 6) and (15, 15)? (a) 16 (b) 225 (c) 15 (d) 21
  2. 2.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
  3. 3.In which quadrant does the point (−8, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  4. 4.What is the distance between the points (4, 8) and (16, 3)? (a) 13 (b) 17 (c) 14 (d) 169
  5. 5.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  6. 6.In which quadrant does the point (9, −8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  7. 7.What is the midpoint of the line joining (9, 13) and (13, 1)? (a) (2, 6) (b) (11, 7) (c) (22, 14) (d) (7, 11)
  8. 8.What is the midpoint of the line joining (7, 17) and (13, 9)? (a) (10, 13) (b) (20, 26) (c) (13, 10) (d) (3, 4)
  9. 9.What is the distance between the points (5, 0) and (11, 8)? (a) 10 (b) 14 (c) 100 (d) 11
  10. 10.What is the distance between the points (8, 7) and (16, 13)? (a) 100 (b) 14 (c) 11 (d) 10
  11. 11.What is the midpoint of the line joining (5, 9) and (7, 17)? (a) (12, 26) (b) (13, 6) (c) (1, 4) (d) (6, 13)
  12. 12.In which quadrant does the point (−9, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  13. 13.What is the distance between the points (2, 14) and (11, 2)? (a) 21 (b) 16 (c) 225 (d) 15
  14. 14.In which quadrant does the point (−4, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  15. 15.In which quadrant does the point (−9, 2) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  16. 16.What is the midpoint of the line joining (0, 6) and (2, 18)? (a) (1, 12) (b) (12, 1) (c) (1, 6) (d) (2, 24)
  17. 17.What is the midpoint of the line joining (6, 5) and (18, 7)? (a) (12, 6) (b) (6, 12) (c) (24, 12) (d) (6, 1)
  18. 18.What is the distance between the points (7, 7) and (31, 14)? (a) 25 (b) 625 (c) 31 (d) 26
  19. 19.What is the midpoint of the line joining (0, 9) and (10, 17)? (a) (5, 13) (b) (10, 26) (c) (5, 4) (d) (13, 5)
  20. 20.What is the midpoint of the line joining (5, 2) and (11, 0)? (a) (1, 8) (b) (8, 1) (c) (3, 1) (d) (16, 2)
  21. 21.In which quadrant does the point (9, 5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  22. 22.In which quadrant does the point (−2, 1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  23. 23.In which quadrant does the point (4, 8) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  24. 24.In which quadrant does the point (3, 2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  25. 25.What is the midpoint of the line joining (8, 3) and (20, 7)? (a) (14, 5) (b) (5, 14) (c) (28, 10) (d) (6, 2)
  26. 26.What is the distance between the points (1, 0) and (10, 12)? (a) 21 (b) 16 (c) 15 (d) 225
  27. 27.What is the midpoint of the line joining (1, 1) and (7, 9)? (a) (8, 10) (b) (5, 4) (c) (4, 5) (d) (3, 4)
  28. 28.In which quadrant does the point (4, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  29. 29.In which quadrant does the point (−4, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  30. 30.What is the midpoint of the line joining (1, 9) and (9, 3)? (a) (6, 5) (b) (4, 3) (c) (10, 12) (d) (5, 6)
  31. 31.What is the distance between the points (1, 17) and (10, 5)? (a) 15 (b) 21 (c) 16 (d) 225
  32. 32.In which quadrant does the point (−6, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  33. 33.What is the distance between the points (1, 15) and (25, 8)? (a) 625 (b) 31 (c) 26 (d) 25
  34. 34.In which quadrant does the point (−6, −5) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  35. 35.What is the midpoint of the line joining (10, 17) and (22, 7)? (a) (12, 16) (b) (32, 24) (c) (16, 12) (d) (6, 5)
  36. 36.What is the midpoint of the line joining (9, 3) and (17, 11)? (a) (13, 7) (b) (26, 14) (c) (4, 4) (d) (7, 13)
  37. 37.What is the distance between the points (3, 12) and (11, 6)? (a) 11 (b) 14 (c) 10 (d) 100
  38. 38.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  39. 39.What is the distance between the points (9, 5) and (12, 9)? (a) 6 (b) 5 (c) 25 (d) 7
  40. 40.What is the distance between the points (7, 24) and (19, 8)? (a) 28 (b) 21 (c) 20 (d) 400

Answer key

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

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