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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 287 · 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 midpoint of the line joining (0, 15) and (2, 5)? (a) (1, 5) (b) (2, 20) (c) (1, 10) (d) (10, 1)
  2. 2.In which quadrant does the point (−7, 6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  3. 3.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 10 (c) 14 (d) 100
  4. 4.What is the distance between the points (6, 7) and (14, 13)? (a) 100 (b) 14 (c) 10 (d) 11
  5. 5.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  6. 6.What is the midpoint of the line joining (10, 6) and (18, 2)? (a) (28, 8) (b) (4, 14) (c) (4, 2) (d) (14, 4)
  7. 7.What is the distance between the points (0, 16) and (5, 4)? (a) 169 (b) 13 (c) 14 (d) 17
  8. 8.What is the midpoint of the line joining (1, 9) and (7, 19)? (a) (3, 5) (b) (8, 28) (c) (14, 4) (d) (4, 14)
  9. 9.What is the distance between the points (9, 7) and (12, 11)? (a) 7 (b) 6 (c) 25 (d) 5
  10. 10.What is the distance between the points (7, 11) and (19, 2)? (a) 225 (b) 16 (c) 21 (d) 15
  11. 11.What is the midpoint of the line joining (3, 4) and (9, 6)? (a) (6, 5) (b) (12, 10) (c) (3, 1) (d) (5, 6)
  12. 12.In which quadrant does the point (9, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  13. 13.What is the distance between the points (1, 15) and (9, 0)? (a) 17 (b) 23 (c) 289 (d) 18
  14. 14.What is the midpoint of the line joining (3, 1) and (15, 3)? (a) (2, 9) (b) (18, 4) (c) (6, 1) (d) (9, 2)
  15. 15.What is the midpoint of the line joining (3, 0) and (5, 10)? (a) (8, 10) (b) (5, 4) (c) (1, 5) (d) (4, 5)
  16. 16.In which quadrant does the point (1, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  17. 17.What is the midpoint of the line joining (1, 0) and (13, 2)? (a) (1, 7) (b) (6, 1) (c) (14, 2) (d) (7, 1)
  18. 18.What is the midpoint of the line joining (4, 9) and (12, 13)? (a) (8, 11) (b) (4, 2) (c) (11, 8) (d) (16, 22)
  19. 19.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  20. 20.In which quadrant does the point (−8, −4) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  21. 21.In which quadrant does the point (3, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  22. 22.How far is the point (15, 8) from the origin (0, 0)? (a) 17 (b) 23 (c) 289 (d) 18
  23. 23.In which quadrant does the point (9, 5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  24. 24.In which quadrant does the point (−5, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  25. 25.In which quadrant does the point (2, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  26. 26.In which quadrant does the point (−9, −3) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  27. 27.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  28. 28.What is the midpoint of the line joining (10, 22) and (14, 10)? (a) (24, 32) (b) (12, 16) (c) (2, 6) (d) (16, 12)
  29. 29.In which quadrant does the point (−8, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  30. 30.In which quadrant does the point (−4, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  31. 31.What is the midpoint of the line joining (7, 1) and (9, 5)? (a) (1, 2) (b) (16, 6) (c) (3, 8) (d) (8, 3)
  32. 32.In which quadrant does the point (−1, 3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  33. 33.In which quadrant does the point (−1, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  34. 34.What is the distance between the points (9, 4) and (21, 20)? (a) 21 (b) 28 (c) 20 (d) 400
  35. 35.What is the midpoint of the line joining (0, 13) and (2, 7)? (a) (1, 3) (b) (2, 20) (c) (10, 1) (d) (1, 10)
  36. 36.What is the distance between the points (8, 12) and (11, 8)? (a) 6 (b) 7 (c) 5 (d) 25
  37. 37.In which quadrant does the point (−7, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  38. 38.What is the distance between the points (4, 7) and (20, 19)? (a) 21 (b) 28 (c) 400 (d) 20
  39. 39.What is the midpoint of the line joining (10, 7) and (12, 13)? (a) (1, 3) (b) (10, 11) (c) (11, 10) (d) (22, 20)
  40. 40.In which quadrant does the point (−6, −9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant

Answer key

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

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