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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 327 · 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 (3, 15) and (7, 5)? (a) (5, 10) (b) (10, 5) (c) (2, 5) (d) (10, 20)
  2. 2.What is the midpoint of the line joining (7, 7) and (13, 5)? (a) (6, 10) (b) (20, 12) (c) (3, 1) (d) (10, 6)
  3. 3.What is the distance between the points (6, 0) and (10, 3)? (a) 5 (b) 6 (c) 25 (d) 7
  4. 4.In which quadrant does the point (1, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  5. 5.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  7. 7.What is the distance between the points (1, 5) and (5, 8)? (a) 25 (b) 6 (c) 7 (d) 5
  8. 8.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  9. 9.What is the midpoint of the line joining (3, 5) and (5, 3)? (a) (5, 4) (b) (8, 8) (c) (1, 1) (d) (4, 4)
  10. 10.What is the distance between the points (1, 2) and (9, 8)? (a) 10 (b) 11 (c) 14 (d) 100
  11. 11.What is the midpoint of the line joining (6, 18) and (14, 8)? (a) (20, 26) (b) (13, 10) (c) (10, 13) (d) (4, 5)
  12. 12.What is the midpoint of the line joining (1, 5) and (3, 13)? (a) (9, 2) (b) (4, 18) (c) (2, 9) (d) (1, 4)
  13. 13.What is the distance between the points (4, 9) and (11, 33)? (a) 26 (b) 31 (c) 25 (d) 625
  14. 14.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 17 (c) 23 (d) 18
  15. 15.What is the midpoint of the line joining (5, 10) and (7, 0)? (a) (12, 10) (b) (5, 6) (c) (6, 5) (d) (1, 5)
  16. 16.What is the distance between the points (2, 0) and (10, 15)? (a) 17 (b) 289 (c) 18 (d) 23
  17. 17.What is the distance between the points (7, 1) and (10, 5)? (a) 25 (b) 6 (c) 7 (d) 5
  18. 18.In which quadrant does the point (1, 7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  19. 19.In which quadrant does the point (6, 3) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  20. 20.What is the distance between the points (6, 9) and (9, 5)? (a) 6 (b) 25 (c) 7 (d) 5
  21. 21.What is the midpoint of the line joining (1, 6) and (11, 14)? (a) (12, 20) (b) (10, 6) (c) (6, 10) (d) (5, 4)
  22. 22.In which quadrant does the point (−1, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  23. 23.What is the distance between the points (6, 14) and (30, 7)? (a) 625 (b) 25 (c) 31 (d) 26
  24. 24.What is the midpoint of the line joining (9, 21) and (11, 9)? (a) (10, 15) (b) (20, 30) (c) (15, 10) (d) (1, 6)
  25. 25.What is the midpoint of the line joining (0, 0) and (8, 12)? (a) (4, 6) (b) (5, 6) (c) (6, 4) (d) (8, 12)
  26. 26.What is the distance between the points (6, 19) and (18, 3)? (a) 400 (b) 20 (c) 21 (d) 28
  27. 27.In which quadrant does the point (2, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  28. 28.What is the midpoint of the line joining (4, 1) and (6, 7)? (a) (5, 4) (b) (1, 3) (c) (10, 8) (d) (4, 5)
  29. 29.In which quadrant does the point (3, −6) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  30. 30.What is the distance between the points (3, 14) and (9, 6)? (a) 14 (b) 100 (c) 11 (d) 10
  31. 31.What is the distance between the points (4, 3) and (7, 7)? (a) 6 (b) 7 (c) 25 (d) 5
  32. 32.What is the distance between the points (7, 32) and (14, 8)? (a) 26 (b) 31 (c) 25 (d) 625
  33. 33.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 31 (d) 625
  34. 34.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  35. 35.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 6 (c) 5 (d) 25
  36. 36.In which quadrant does the point (1, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  37. 37.What is the midpoint of the line joining (6, 5) and (14, 3)? (a) (4, 1) (b) (4, 10) (c) (20, 8) (d) (10, 4)
  38. 38.What is the distance between the points (5, 14) and (21, 2)? (a) 400 (b) 28 (c) 21 (d) 20
  39. 39.What is the midpoint of the line joining (2, 3) and (6, 11)? (a) (8, 14) (b) (2, 4) (c) (4, 7) (d) (7, 4)
  40. 40.What is the distance between the points (1, 21) and (10, 9)? (a) 225 (b) 16 (c) 15 (d) 21

Answer key

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

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