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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 537 · 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) 100 (c) 11 (d) 14
  2. 2.What is the midpoint of the line joining (1, 0) and (7, 4)? (a) (8, 4) (b) (4, 2) (c) (3, 2) (d) (2, 4)
  3. 3.What is the midpoint of the line joining (2, 10) and (12, 2)? (a) (7, 6) (b) (5, 4) (c) (14, 12) (d) (6, 7)
  4. 4.In which quadrant does the point (9, −3) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  5. 5.In which quadrant does the point (−4, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  6. 6.What is the distance between the points (8, 2) and (32, 9)? (a) 25 (b) 26 (c) 625 (d) 31
  7. 7.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  8. 8.What is the midpoint of the line joining (4, 8) and (12, 12)? (a) (10, 8) (b) (4, 2) (c) (8, 10) (d) (16, 20)
  9. 9.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  10. 10.In which quadrant does the point (1, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  11. 11.What is the midpoint of the line joining (10, 6) and (18, 18)? (a) (12, 14) (b) (14, 12) (c) (4, 6) (d) (28, 24)
  12. 12.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  13. 13.What is the midpoint of the line joining (2, 13) and (14, 1)? (a) (7, 8) (b) (16, 14) (c) (6, 6) (d) (8, 7)
  14. 14.What is the midpoint of the line joining (1, 16) and (3, 4)? (a) (1, 6) (b) (4, 20) (c) (2, 10) (d) (10, 2)
  15. 15.What is the midpoint of the line joining (8, 14) and (16, 4)? (a) (24, 18) (b) (4, 5) (c) (12, 9) (d) (9, 12)
  16. 16.What is the midpoint of the line joining (0, 16) and (12, 4)? (a) (10, 6) (b) (6, 10) (c) (12, 20) (d) (6, 6)
  17. 17.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  18. 18.What is the distance between the points (6, 5) and (9, 9)? (a) 7 (b) 6 (c) 25 (d) 5
  19. 19.In which quadrant does the point (−3, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  20. 20.What is the distance between the points (8, 8) and (14, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  21. 21.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 6 (c) 7 (d) 25
  22. 22.In which quadrant does the point (2, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  23. 23.What is the midpoint of the line joining (1, 10) and (3, 12)? (a) (2, 11) (b) (4, 22) (c) (11, 2) (d) (1, 1)
  24. 24.In which quadrant does the point (−2, −4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  25. 25.What is the midpoint of the line joining (3, 4) and (5, 6)? (a) (5, 4) (b) (8, 10) (c) (1, 1) (d) (4, 5)
  26. 26.In which quadrant does the point (−4, 9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  27. 27.In which quadrant does the point (5, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  28. 28.What is the distance between the points (8, 0) and (12, 3)? (a) 7 (b) 6 (c) 5 (d) 25
  29. 29.In which quadrant does the point (5, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  30. 30.What is the midpoint of the line joining (5, 8) and (9, 4)? (a) (6, 7) (b) (2, 2) (c) (14, 12) (d) (7, 6)
  31. 31.In which quadrant does the point (−2, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  32. 32.How far is the point (12, 9) from the origin (0, 0)? (a) 15 (b) 225 (c) 16 (d) 21
  33. 33.What is the distance between the points (3, 23) and (15, 7)? (a) 28 (b) 21 (c) 400 (d) 20
  34. 34.In which quadrant does the point (1, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  35. 35.What is the midpoint of the line joining (8, 16) and (12, 8)? (a) (12, 10) (b) (20, 24) (c) (10, 12) (d) (2, 4)
  36. 36.What is the midpoint of the line joining (8, 3) and (20, 5)? (a) (14, 4) (b) (4, 14) (c) (6, 1) (d) (28, 8)
  37. 37.In which quadrant does the point (4, 4) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  38. 38.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  39. 39.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 21 (c) 28 (d) 400
  40. 40.What is the distance between the points (6, 1) and (13, 25)? (a) 625 (b) 25 (c) 31 (d) 26

Answer key

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

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