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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 918 · 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 (1, 0) and (13, 12)? (a) (14, 12) (b) (6, 6) (c) (6, 7) (d) (7, 6)
  2. 2.In which quadrant does the point (3, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  3. 3.In which quadrant does the point (9, −9) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  4. 4.What is the distance between the points (6, 9) and (11, 21)? (a) 13 (b) 17 (c) 14 (d) 169
  5. 5.What is the midpoint of the line joining (2, 2) and (10, 12)? (a) (6, 7) (b) (4, 5) (c) (7, 6) (d) (12, 14)
  6. 6.What is the distance between the points (0, 13) and (12, 8)? (a) 13 (b) 17 (c) 169 (d) 14
  7. 7.What is the midpoint of the line joining (1, 5) and (9, 1)? (a) (4, 2) (b) (3, 5) (c) (10, 6) (d) (5, 3)
  8. 8.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  9. 9.What is the midpoint of the line joining (0, 16) and (2, 6)? (a) (11, 1) (b) (1, 11) (c) (1, 5) (d) (2, 22)
  10. 10.What is the midpoint of the line joining (6, 6) and (14, 0)? (a) (3, 10) (b) (10, 3) (c) (4, 3) (d) (20, 6)
  11. 11.In which quadrant does the point (−3, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  12. 12.What is the distance between the points (1, 3) and (8, 27)? (a) 625 (b) 31 (c) 26 (d) 25
  13. 13.What is the distance between the points (3, 6) and (15, 15)? (a) 225 (b) 16 (c) 21 (d) 15
  14. 14.In which quadrant does the point (−1, 9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  15. 15.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
  16. 16.In which quadrant does the point (4, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  17. 17.What is the distance between the points (8, 10) and (20, 5)? (a) 17 (b) 169 (c) 14 (d) 13
  18. 18.What is the midpoint of the line joining (8, 13) and (10, 7)? (a) (10, 9) (b) (18, 20) (c) (9, 10) (d) (1, 3)
  19. 19.In which quadrant does the point (4, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  20. 20.In which quadrant does the point (−2, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  21. 21.What is the midpoint of the line joining (8, 8) and (12, 20)? (a) (14, 10) (b) (2, 6) (c) (10, 14) (d) (20, 28)
  22. 22.In which quadrant does the point (−4, −8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  23. 23.What is the midpoint of the line joining (1, 16) and (7, 10)? (a) (8, 26) (b) (3, 3) (c) (4, 13) (d) (13, 4)
  24. 24.In which quadrant does the point (−9, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  25. 25.What is the distance between the points (0, 15) and (12, 6)? (a) 225 (b) 21 (c) 15 (d) 16
  26. 26.What is the midpoint of the line joining (5, 3) and (11, 9)? (a) (3, 3) (b) (16, 12) (c) (8, 6) (d) (6, 8)
  27. 27.In which quadrant does the point (−1, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  28. 28.In which quadrant does the point (1, 2) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  29. 29.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 10 (c) 100 (d) 11
  30. 30.In which quadrant does the point (1, −4) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  31. 31.What is the midpoint of the line joining (6, 6) and (12, 4)? (a) (9, 5) (b) (5, 9) (c) (3, 1) (d) (18, 10)
  32. 32.What is the distance between the points (5, 2) and (13, 17)? (a) 18 (b) 17 (c) 23 (d) 289
  33. 33.What is the distance between the points (2, 5) and (7, 17)? (a) 14 (b) 17 (c) 169 (d) 13
  34. 34.What is the distance between the points (5, 13) and (20, 5)? (a) 17 (b) 289 (c) 23 (d) 18
  35. 35.What is the midpoint of the line joining (10, 0) and (16, 12)? (a) (3, 6) (b) (6, 13) (c) (26, 12) (d) (13, 6)
  36. 36.What is the distance between the points (8, 2) and (24, 14)? (a) 28 (b) 21 (c) 400 (d) 20
  37. 37.What is the distance between the points (3, 19) and (19, 7)? (a) 400 (b) 28 (c) 21 (d) 20
  38. 38.What is the distance between the points (1, 24) and (13, 8)? (a) 28 (b) 21 (c) 20 (d) 400
  39. 39.In which quadrant does the point (−6, 1) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  40. 40.What is the midpoint of the line joining (2, 6) and (8, 4)? (a) (5, 5) (b) (10, 10) (c) (3, 1) (d) (6, 5)

Answer key

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

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