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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 168 · 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, −9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  2. 2.What is the midpoint of the line joining (10, 16) and (14, 4)? (a) (2, 6) (b) (12, 10) (c) (10, 12) (d) (24, 20)
  3. 3.What is the midpoint of the line joining (1, 11) and (7, 3)? (a) (7, 4) (b) (3, 4) (c) (4, 7) (d) (8, 14)
  4. 4.What is the distance between the points (4, 8) and (16, 13)? (a) 169 (b) 17 (c) 14 (d) 13
  5. 5.What is the distance between the points (6, 7) and (10, 4)? (a) 7 (b) 25 (c) 6 (d) 5
  6. 6.What is the midpoint of the line joining (8, 7) and (10, 11)? (a) (18, 18) (b) (1, 2) (c) (9, 9) (d) (10, 9)
  7. 7.What is the distance between the points (3, 1) and (7, 4)? (a) 7 (b) 6 (c) 25 (d) 5
  8. 8.In which quadrant does the point (7, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  9. 9.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  10. 10.In which quadrant does the point (−8, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  11. 11.What is the distance between the points (2, 1) and (8, 9)? (a) 14 (b) 11 (c) 10 (d) 100
  12. 12.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  13. 13.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  14. 14.What is the midpoint of the line joining (1, 2) and (3, 8)? (a) (2, 5) (b) (4, 10) (c) (1, 3) (d) (5, 2)
  15. 15.What is the midpoint of the line joining (8, 8) and (20, 10)? (a) (6, 1) (b) (9, 14) (c) (28, 18) (d) (14, 9)
  16. 16.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 25 (c) 6 (d) 7
  17. 17.What is the distance between the points (1, 10) and (13, 5)? (a) 14 (b) 169 (c) 17 (d) 13
  18. 18.What is the distance between the points (0, 3) and (4, 6)? (a) 25 (b) 7 (c) 5 (d) 6
  19. 19.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 17 (c) 18 (d) 289
  20. 20.What is the distance between the points (6, 3) and (18, 8)? (a) 14 (b) 13 (c) 17 (d) 169
  21. 21.In which quadrant does the point (7, −1) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  22. 22.In which quadrant does the point (1, 4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  23. 23.What is the distance between the points (1, 9) and (8, 33)? (a) 625 (b) 26 (c) 31 (d) 25
  24. 24.In which quadrant does the point (3, −6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  25. 25.In which quadrant does the point (7, 4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.What is the midpoint of the line joining (0, 10) and (4, 0)? (a) (2, 5) (b) (3, 5) (c) (5, 2) (d) (4, 10)
  27. 27.In which quadrant does the point (4, −3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  28. 28.What is the distance between the points (1, 15) and (7, 7)? (a) 11 (b) 10 (c) 14 (d) 100
  29. 29.What is the midpoint of the line joining (1, 0) and (13, 10)? (a) (6, 5) (b) (7, 5) (c) (14, 10) (d) (5, 7)
  30. 30.In which quadrant does the point (1, 7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  31. 31.What is the distance between the points (3, 4) and (11, 10)? (a) 11 (b) 100 (c) 10 (d) 14
  32. 32.In which quadrant does the point (−2, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  33. 33.What is the distance between the points (0, 7) and (6, 15)? (a) 10 (b) 100 (c) 11 (d) 14
  34. 34.What is the distance between the points (6, 5) and (9, 9)? (a) 25 (b) 6 (c) 7 (d) 5
  35. 35.In which quadrant does the point (−6, 8) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  36. 36.What is the midpoint of the line joining (0, 0) and (10, 12)? (a) (5, 6) (b) (6, 6) (c) (10, 12) (d) (6, 5)
  37. 37.What is the distance between the points (2, 17) and (17, 9)? (a) 23 (b) 289 (c) 18 (d) 17
  38. 38.What is the midpoint of the line joining (10, 8) and (16, 0)? (a) (26, 8) (b) (4, 13) (c) (3, 4) (d) (13, 4)
  39. 39.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  40. 40.What is the distance between the points (6, 6) and (14, 21)? (a) 17 (b) 18 (c) 289 (d) 23

Answer key

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

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