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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 104 · 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.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 11 (c) 14 (d) 100
  2. 2.What is the midpoint of the line joining (6, 22) and (12, 10)? (a) (3, 6) (b) (16, 9) (c) (18, 32) (d) (9, 16)
  3. 3.In which quadrant does the point (−2, 5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  4. 4.What is the distance between the points (5, 3) and (10, 15)? (a) 14 (b) 169 (c) 17 (d) 13
  5. 5.What is the distance between the points (2, 8) and (14, 24)? (a) 20 (b) 400 (c) 28 (d) 21
  6. 6.In which quadrant does the point (2, −1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  7. 7.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 625 (d) 25
  8. 8.What is the midpoint of the line joining (6, 1) and (12, 7)? (a) (18, 8) (b) (9, 4) (c) (4, 9) (d) (3, 3)
  9. 9.What is the midpoint of the line joining (1, 22) and (11, 10)? (a) (5, 6) (b) (16, 6) (c) (12, 32) (d) (6, 16)
  10. 10.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  11. 11.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  12. 12.In which quadrant does the point (−1, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  13. 13.What is the distance between the points (9, 4) and (13, 1)? (a) 5 (b) 6 (c) 7 (d) 25
  14. 14.What is the distance between the points (9, 8) and (14, 20)? (a) 169 (b) 14 (c) 13 (d) 17
  15. 15.In which quadrant does the point (5, −4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  16. 16.What is the midpoint of the line joining (6, 3) and (8, 5)? (a) (1, 1) (b) (14, 8) (c) (4, 7) (d) (7, 4)
  17. 17.What is the midpoint of the line joining (2, 0) and (12, 6)? (a) (7, 3) (b) (14, 6) (c) (5, 3) (d) (3, 7)
  18. 18.What is the distance between the points (7, 16) and (12, 4)? (a) 14 (b) 13 (c) 169 (d) 17
  19. 19.What is the distance between the points (6, 9) and (9, 13)? (a) 25 (b) 6 (c) 5 (d) 7
  20. 20.What is the distance between the points (5, 13) and (20, 5)? (a) 289 (b) 23 (c) 18 (d) 17
  21. 21.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 21 (d) 225
  22. 22.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 21 (c) 20 (d) 400
  23. 23.What is the distance between the points (7, 4) and (11, 7)? (a) 7 (b) 25 (c) 6 (d) 5
  24. 24.What is the midpoint of the line joining (8, 8) and (14, 12)? (a) (3, 2) (b) (22, 20) (c) (11, 10) (d) (10, 11)
  25. 25.In which quadrant does the point (1, −2) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  26. 26.What is the midpoint of the line joining (4, 5) and (16, 11)? (a) (8, 10) (b) (10, 8) (c) (20, 16) (d) (6, 3)
  27. 27.In which quadrant does the point (−8, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  28. 28.In which quadrant does the point (−7, −3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  29. 29.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 16 (c) 15 (d) 21
  30. 30.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  31. 31.In which quadrant does the point (2, −8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  32. 32.What is the distance between the points (2, 10) and (26, 3)? (a) 26 (b) 625 (c) 31 (d) 25
  33. 33.What is the midpoint of the line joining (10, 4) and (18, 14)? (a) (9, 14) (b) (4, 5) (c) (28, 18) (d) (14, 9)
  34. 34.In which quadrant does the point (−4, −4) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  35. 35.What is the distance between the points (4, 6) and (7, 2)? (a) 7 (b) 6 (c) 5 (d) 25
  36. 36.What is the distance between the points (2, 9) and (5, 5)? (a) 6 (b) 7 (c) 25 (d) 5
  37. 37.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 169 (c) 17 (d) 14
  38. 38.What is the distance between the points (4, 11) and (16, 2)? (a) 21 (b) 15 (c) 16 (d) 225
  39. 39.What is the midpoint of the line joining (2, 6) and (8, 0)? (a) (10, 6) (b) (3, 3) (c) (5, 3) (d) (3, 5)
  40. 40.What is the midpoint of the line joining (8, 0) and (16, 12)? (a) (12, 6) (b) (4, 6) (c) (6, 12) (d) (24, 12)

Answer key

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

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