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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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