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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 264 · 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, 13) and (10, 5)? (a) (12, 18) (b) (9, 6) (c) (4, 4) (d) (6, 9)
  2. 2.What is the distance between the points (8, 12) and (20, 3)? (a) 15 (b) 16 (c) 225 (d) 21
  3. 3.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  4. 4.In which quadrant does the point (−3, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  5. 5.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  6. 6.What is the distance between the points (4, 2) and (12, 8)? (a) 100 (b) 10 (c) 11 (d) 14
  7. 7.What is the midpoint of the line joining (9, 0) and (13, 10)? (a) (2, 5) (b) (11, 5) (c) (5, 11) (d) (22, 10)
  8. 8.What is the distance between the points (9, 4) and (17, 19)? (a) 18 (b) 17 (c) 23 (d) 289
  9. 9.What is the midpoint of the line joining (3, 11) and (5, 9)? (a) (8, 20) (b) (10, 4) (c) (1, 1) (d) (4, 10)
  10. 10.What is the distance between the points (7, 7) and (31, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  11. 11.How far is the point (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 20 (d) 21
  12. 12.In which quadrant does the point (−4, −7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  13. 13.What is the distance between the points (4, 13) and (28, 6)? (a) 625 (b) 25 (c) 31 (d) 26
  14. 14.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  15. 15.What is the midpoint of the line joining (10, 10) and (22, 2)? (a) (16, 6) (b) (6, 4) (c) (6, 16) (d) (32, 12)
  16. 16.In which quadrant does the point (4, 1) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  17. 17.In which quadrant does the point (1, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  18. 18.What is the distance between the points (7, 0) and (13, 8)? (a) 10 (b) 100 (c) 11 (d) 14
  19. 19.What is the distance between the points (9, 0) and (12, 4)? (a) 6 (b) 7 (c) 5 (d) 25
  20. 20.What is the distance between the points (6, 12) and (15, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  21. 21.What is the distance between the points (0, 28) and (7, 4)? (a) 31 (b) 25 (c) 26 (d) 625
  22. 22.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 31 (d) 25
  23. 23.What is the midpoint of the line joining (4, 5) and (12, 15)? (a) (10, 8) (b) (8, 10) (c) (4, 5) (d) (16, 20)
  24. 24.In which quadrant does the point (5, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  25. 25.In which quadrant does the point (7, 4) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  26. 26.In which quadrant does the point (4, −4) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  27. 27.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  28. 28.What is the midpoint of the line joining (0, 4) and (8, 14)? (a) (8, 18) (b) (4, 9) (c) (4, 5) (d) (9, 4)
  29. 29.What is the distance between the points (1, 1) and (9, 16)? (a) 289 (b) 23 (c) 18 (d) 17
  30. 30.What is the distance between the points (3, 4) and (12, 16)? (a) 21 (b) 16 (c) 225 (d) 15
  31. 31.What is the midpoint of the line joining (5, 8) and (11, 14)? (a) (3, 3) (b) (16, 22) (c) (8, 11) (d) (11, 8)
  32. 32.What is the distance between the points (0, 11) and (24, 4)? (a) 26 (b) 25 (c) 625 (d) 31
  33. 33.In which quadrant does the point (−3, 6) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  34. 34.What is the distance between the points (7, 17) and (23, 5)? (a) 21 (b) 28 (c) 400 (d) 20
  35. 35.What is the midpoint of the line joining (9, 10) and (11, 6)? (a) (10, 8) (b) (20, 16) (c) (1, 2) (d) (8, 10)
  36. 36.What is the midpoint of the line joining (0, 5) and (8, 17)? (a) (4, 6) (b) (4, 11) (c) (8, 22) (d) (11, 4)
  37. 37.What is the midpoint of the line joining (3, 4) and (7, 2)? (a) (3, 5) (b) (5, 3) (c) (10, 6) (d) (2, 1)
  38. 38.In which quadrant does the point (−8, 8) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  39. 39.What is the midpoint of the line joining (0, 10) and (6, 8)? (a) (9, 3) (b) (6, 18) (c) (3, 1) (d) (3, 9)
  40. 40.What is the midpoint of the line joining (7, 17) and (11, 5)? (a) (18, 22) (b) (9, 11) (c) (2, 6) (d) (11, 9)

Answer key

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

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