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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 389 · 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 (5, 6) and (13, 12)? (a) 10 (b) 14 (c) 11 (d) 100
  2. 2.What is the distance between the points (0, 9) and (4, 12)? (a) 7 (b) 5 (c) 25 (d) 6
  3. 3.What is the midpoint of the line joining (1, 7) and (9, 1)? (a) (10, 8) (b) (4, 5) (c) (4, 3) (d) (5, 4)
  4. 4.What is the midpoint of the line joining (4, 6) and (16, 12)? (a) (9, 10) (b) (6, 3) (c) (20, 18) (d) (10, 9)
  5. 5.What is the midpoint of the line joining (1, 8) and (9, 18)? (a) (4, 5) (b) (10, 26) (c) (5, 13) (d) (13, 5)
  6. 6.What is the midpoint of the line joining (2, 3) and (14, 15)? (a) (9, 8) (b) (8, 9) (c) (16, 18) (d) (6, 6)
  7. 7.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  8. 8.What is the midpoint of the line joining (10, 3) and (16, 1)? (a) (3, 1) (b) (2, 13) (c) (26, 4) (d) (13, 2)
  9. 9.In which quadrant does the point (5, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  10. 10.In which quadrant does the point (6, −2) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  11. 11.In which quadrant does the point (−2, 8) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  12. 12.What is the distance between the points (9, 2) and (24, 10)? (a) 23 (b) 18 (c) 17 (d) 289
  13. 13.What is the midpoint of the line joining (1, 10) and (9, 2)? (a) (5, 6) (b) (10, 12) (c) (4, 4) (d) (6, 5)
  14. 14.What is the distance between the points (6, 3) and (15, 15)? (a) 225 (b) 16 (c) 21 (d) 15
  15. 15.In which quadrant does the point (−7, 5) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  16. 16.What is the midpoint of the line joining (0, 1) and (12, 9)? (a) (6, 4) (b) (12, 10) (c) (5, 6) (d) (6, 5)
  17. 17.What is the distance between the points (9, 1) and (25, 13)? (a) 400 (b) 28 (c) 21 (d) 20
  18. 18.In which quadrant does the point (−6, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  19. 19.What is the midpoint of the line joining (2, 12) and (14, 2)? (a) (7, 8) (b) (6, 5) (c) (8, 7) (d) (16, 14)
  20. 20.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 20 (d) 400
  21. 21.In which quadrant does the point (3, −5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  22. 22.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
  23. 23.What is the distance between the points (1, 17) and (9, 2)? (a) 17 (b) 18 (c) 289 (d) 23
  24. 24.In which quadrant does the point (−6, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  25. 25.In which quadrant does the point (−2, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  26. 26.What is the distance between the points (0, 3) and (16, 15)? (a) 20 (b) 28 (c) 21 (d) 400
  27. 27.What is the midpoint of the line joining (9, 2) and (19, 10)? (a) (14, 6) (b) (28, 12) (c) (6, 14) (d) (5, 4)
  28. 28.What is the distance between the points (7, 8) and (12, 20)? (a) 14 (b) 17 (c) 13 (d) 169
  29. 29.What is the distance between the points (4, 2) and (10, 10)? (a) 11 (b) 100 (c) 10 (d) 14
  30. 30.What is the distance between the points (2, 19) and (7, 7)? (a) 169 (b) 14 (c) 17 (d) 13
  31. 31.What is the midpoint of the line joining (9, 2) and (19, 6)? (a) (14, 4) (b) (4, 14) (c) (28, 8) (d) (5, 2)
  32. 32.What is the distance between the points (7, 2) and (11, 5)? (a) 25 (b) 7 (c) 6 (d) 5
  33. 33.In which quadrant does the point (−5, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  34. 34.In which quadrant does the point (8, 2) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  35. 35.What is the distance between the points (3, 1) and (11, 7)? (a) 11 (b) 100 (c) 10 (d) 14
  36. 36.What is the midpoint of the line joining (7, 6) and (13, 0)? (a) (20, 6) (b) (3, 3) (c) (3, 10) (d) (10, 3)
  37. 37.In which quadrant does the point (6, 6) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  38. 38.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  39. 39.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  40. 40.What is the midpoint of the line joining (8, 10) and (20, 0)? (a) (6, 5) (b) (14, 5) (c) (5, 14) (d) (28, 10)

Answer key

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

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