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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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