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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 11 · 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, 7) and (12, 3)? (a) (5, 2) (b) (7, 5) (c) (5, 7) (d) (14, 10)
  2. 2.In which quadrant does the point (5, 8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  3. 3.What is the distance between the points (0, 26) and (7, 2)? (a) 31 (b) 26 (c) 625 (d) 25
  4. 4.What is the midpoint of the line joining (7, 13) and (13, 3)? (a) (8, 10) (b) (20, 16) (c) (3, 5) (d) (10, 8)
  5. 5.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  6. 6.What is the midpoint of the line joining (2, 0) and (14, 10)? (a) (5, 8) (b) (16, 10) (c) (6, 5) (d) (8, 5)
  7. 7.What is the midpoint of the line joining (10, 1) and (22, 7)? (a) (32, 8) (b) (16, 4) (c) (4, 16) (d) (6, 3)
  8. 8.What is the distance between the points (7, 14) and (15, 8)? (a) 11 (b) 100 (c) 10 (d) 14
  9. 9.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 17 (d) 18
  10. 10.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  11. 11.What is the midpoint of the line joining (2, 2) and (8, 0)? (a) (5, 1) (b) (1, 5) (c) (3, 1) (d) (10, 2)
  12. 12.In which quadrant does the point (−3, 6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  13. 13.What is the distance between the points (3, 13) and (12, 1)? (a) 15 (b) 225 (c) 16 (d) 21
  14. 14.What is the midpoint of the line joining (6, 10) and (8, 12)? (a) (14, 22) (b) (7, 11) (c) (1, 1) (d) (11, 7)
  15. 15.What is the midpoint of the line joining (0, 10) and (12, 18)? (a) (6, 14) (b) (12, 28) (c) (14, 6) (d) (6, 4)
  16. 16.What is the midpoint of the line joining (9, 18) and (13, 6)? (a) (12, 11) (b) (11, 12) (c) (2, 6) (d) (22, 24)
  17. 17.What is the distance between the points (1, 4) and (17, 16)? (a) 28 (b) 400 (c) 20 (d) 21
  18. 18.In which quadrant does the point (−1, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  19. 19.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 10 (d) 11
  20. 20.In which quadrant does the point (9, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  21. 21.What is the distance between the points (9, 9) and (12, 13)? (a) 25 (b) 6 (c) 7 (d) 5
  22. 22.What is the midpoint of the line joining (0, 2) and (10, 4)? (a) (5, 1) (b) (3, 5) (c) (5, 3) (d) (10, 6)
  23. 23.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  24. 24.In which quadrant does the point (−6, −4) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  25. 25.What is the midpoint of the line joining (4, 12) and (8, 10)? (a) (11, 6) (b) (6, 11) (c) (2, 1) (d) (12, 22)
  26. 26.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  27. 27.What is the midpoint of the line joining (4, 9) and (16, 1)? (a) (5, 10) (b) (10, 5) (c) (6, 4) (d) (20, 10)
  28. 28.What is the midpoint of the line joining (0, 10) and (6, 4)? (a) (3, 3) (b) (7, 3) (c) (6, 14) (d) (3, 7)
  29. 29.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 26 (d) 625
  30. 30.What is the distance between the points (3, 8) and (15, 24)? (a) 28 (b) 400 (c) 20 (d) 21
  31. 31.In which quadrant does the point (6, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  32. 32.What is the distance between the points (2, 11) and (10, 5)? (a) 14 (b) 10 (c) 11 (d) 100
  33. 33.What is the midpoint of the line joining (9, 0) and (11, 10)? (a) (5, 10) (b) (1, 5) (c) (10, 5) (d) (20, 10)
  34. 34.In which quadrant does the point (−1, 1) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  35. 35.What is the distance between the points (1, 0) and (4, 4)? (a) 7 (b) 6 (c) 5 (d) 25
  36. 36.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 31 (c) 25 (d) 625
  37. 37.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  38. 38.What is the distance between the points (8, 11) and (14, 3)? (a) 10 (b) 11 (c) 14 (d) 100
  39. 39.In which quadrant does the point (5, 5) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  40. 40.In which quadrant does the point (9, −3) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant

Answer key

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

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