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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 936 · 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 (0, 14) and (8, 10)? (a) (12, 4) (b) (8, 24) (c) (4, 12) (d) (4, 2)
  2. 2.What is the midpoint of the line joining (8, 6) and (20, 14)? (a) (6, 4) (b) (10, 14) (c) (28, 20) (d) (14, 10)
  3. 3.What is the distance between the points (6, 7) and (30, 14)? (a) 625 (b) 26 (c) 25 (d) 31
  4. 4.What is the midpoint of the line joining (1, 7) and (5, 11)? (a) (3, 9) (b) (6, 18) (c) (2, 2) (d) (9, 3)
  5. 5.What is the midpoint of the line joining (5, 0) and (11, 12)? (a) (16, 12) (b) (8, 6) (c) (6, 8) (d) (3, 6)
  6. 6.In which quadrant does the point (9, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  7. 7.What is the midpoint of the line joining (7, 4) and (13, 16)? (a) (10, 10) (b) (20, 20) (c) (11, 10) (d) (3, 6)
  8. 8.What is the midpoint of the line joining (0, 1) and (10, 3)? (a) (5, 1) (b) (10, 4) (c) (2, 5) (d) (5, 2)
  9. 9.What is the midpoint of the line joining (7, 2) and (11, 10)? (a) (18, 12) (b) (2, 4) (c) (6, 9) (d) (9, 6)
  10. 10.What is the midpoint of the line joining (1, 8) and (9, 12)? (a) (10, 5) (b) (5, 10) (c) (4, 2) (d) (10, 20)
  11. 11.In which quadrant does the point (−6, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  12. 12.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  13. 13.What is the midpoint of the line joining (5, 16) and (15, 4)? (a) (5, 6) (b) (11, 10) (c) (10, 10) (d) (20, 20)
  14. 14.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 21 (c) 16 (d) 225
  15. 15.What is the distance between the points (9, 5) and (25, 17)? (a) 21 (b) 400 (c) 28 (d) 20
  16. 16.In which quadrant does the point (−9, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  17. 17.In which quadrant does the point (9, 3) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  18. 18.In which quadrant does the point (−9, 4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  19. 19.What is the distance between the points (4, 17) and (10, 9)? (a) 10 (b) 11 (c) 100 (d) 14
  20. 20.What is the midpoint of the line joining (0, 1) and (8, 7)? (a) (8, 8) (b) (4, 4) (c) (4, 3) (d) (5, 4)
  21. 21.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  22. 22.In which quadrant does the point (−4, −3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  23. 23.What is the midpoint of the line joining (3, 10) and (11, 12)? (a) (4, 1) (b) (14, 22) (c) (11, 7) (d) (7, 11)
  24. 24.In which quadrant does the point (1, 4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  25. 25.In which quadrant does the point (−2, 5) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.In which quadrant does the point (5, −8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  27. 27.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  28. 28.What is the midpoint of the line joining (4, 4) and (10, 12)? (a) (3, 4) (b) (14, 16) (c) (8, 7) (d) (7, 8)
  29. 29.How far is the point (16, 12) from the origin (0, 0)? (a) 21 (b) 20 (c) 28 (d) 400
  30. 30.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  31. 31.What is the midpoint of the line joining (6, 8) and (10, 0)? (a) (16, 8) (b) (4, 8) (c) (2, 4) (d) (8, 4)
  32. 32.What is the distance between the points (6, 15) and (14, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  33. 33.In which quadrant does the point (6, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  34. 34.What is the midpoint of the line joining (1, 0) and (11, 2)? (a) (12, 2) (b) (1, 6) (c) (5, 1) (d) (6, 1)
  35. 35.In which quadrant does the point (8, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  36. 36.In which quadrant does the point (7, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  37. 37.What is the distance between the points (4, 9) and (7, 13)? (a) 5 (b) 6 (c) 25 (d) 7
  38. 38.In which quadrant does the point (2, 7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  39. 39.What is the midpoint of the line joining (6, 22) and (18, 10)? (a) (16, 12) (b) (6, 6) (c) (12, 16) (d) (24, 32)
  40. 40.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 7 (d) 5

Answer key

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

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