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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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