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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 373 · 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 (1, 24) and (13, 8)? (a) 21 (b) 20 (c) 400 (d) 28
  2. 2.In which quadrant does the point (−2, 7) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  3. 3.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  4. 4.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  5. 5.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  7. 7.What is the distance between the points (0, 0) and (3, 4)? (a) 7 (b) 25 (c) 5 (d) 6
  8. 8.What is the midpoint of the line joining (1, 6) and (9, 4)? (a) (4, 1) (b) (10, 10) (c) (6, 5) (d) (5, 5)
  9. 9.What is the distance between the points (7, 6) and (15, 12)? (a) 14 (b) 10 (c) 100 (d) 11
  10. 10.What is the distance between the points (6, 6) and (10, 9)? (a) 5 (b) 6 (c) 7 (d) 25
  11. 11.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5
  12. 12.What is the distance between the points (1, 0) and (13, 9)? (a) 21 (b) 16 (c) 225 (d) 15
  13. 13.What is the midpoint of the line joining (3, 4) and (9, 14)? (a) (3, 5) (b) (9, 6) (c) (12, 18) (d) (6, 9)
  14. 14.In which quadrant does the point (5, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  15. 15.What is the midpoint of the line joining (9, 1) and (11, 5)? (a) (20, 6) (b) (3, 10) (c) (10, 3) (d) (1, 2)
  16. 16.What is the midpoint of the line joining (4, 1) and (16, 11)? (a) (6, 5) (b) (20, 12) (c) (10, 6) (d) (6, 10)
  17. 17.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  18. 18.What is the midpoint of the line joining (6, 14) and (10, 10)? (a) (12, 8) (b) (2, 2) (c) (8, 12) (d) (16, 24)
  19. 19.In which quadrant does the point (−5, −2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  20. 20.What is the midpoint of the line joining (8, 17) and (10, 7)? (a) (1, 5) (b) (12, 9) (c) (18, 24) (d) (9, 12)
  21. 21.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  22. 22.In which quadrant does the point (−3, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  23. 23.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 20 (c) 400 (d) 28
  24. 24.What is the distance between the points (7, 0) and (14, 24)? (a) 25 (b) 26 (c) 625 (d) 31
  25. 25.What is the midpoint of the line joining (2, 16) and (12, 10)? (a) (13, 7) (b) (7, 13) (c) (5, 3) (d) (14, 26)
  26. 26.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  27. 27.What is the midpoint of the line joining (0, 1) and (12, 13)? (a) (7, 6) (b) (6, 6) (c) (12, 14) (d) (6, 7)
  28. 28.What is the distance between the points (1, 0) and (9, 15)? (a) 23 (b) 18 (c) 17 (d) 289
  29. 29.In which quadrant does the point (−5, −4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  30. 30.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 31 (d) 26
  31. 31.In which quadrant does the point (−6, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  32. 32.What is the midpoint of the line joining (8, 0) and (20, 6)? (a) (3, 14) (b) (28, 6) (c) (6, 3) (d) (14, 3)
  33. 33.In which quadrant does the point (6, −1) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  34. 34.What is the distance between the points (6, 20) and (15, 8)? (a) 225 (b) 21 (c) 16 (d) 15
  35. 35.What is the distance between the points (2, 8) and (18, 20)? (a) 20 (b) 21 (c) 28 (d) 400
  36. 36.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 21 (d) 400
  37. 37.In which quadrant does the point (6, −5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  38. 38.In which quadrant does the point (−1, −8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  39. 39.In which quadrant does the point (7, 5) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  40. 40.In which quadrant does the point (6, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant

Answer key

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

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