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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 120 · 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 (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  2. 2.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 5 (c) 7 (d) 6
  3. 3.What is the distance between the points (2, 4) and (5, 0)? (a) 5 (b) 7 (c) 6 (d) 25
  4. 4.What is the midpoint of the line joining (6, 17) and (12, 9)? (a) (13, 9) (b) (18, 26) (c) (9, 13) (d) (3, 4)
  5. 5.How far is the point (16, 12) from the origin (0, 0)? (a) 20 (b) 28 (c) 400 (d) 21
  6. 6.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  7. 7.What is the distance between the points (0, 16) and (6, 8)? (a) 100 (b) 14 (c) 10 (d) 11
  8. 8.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 14 (d) 10
  9. 9.What is the midpoint of the line joining (7, 18) and (9, 6)? (a) (1, 6) (b) (12, 8) (c) (16, 24) (d) (8, 12)
  10. 10.What is the midpoint of the line joining (5, 5) and (17, 9)? (a) (11, 7) (b) (6, 2) (c) (22, 14) (d) (7, 11)
  11. 11.In which quadrant does the point (2, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  12. 12.What is the midpoint of the line joining (10, 0) and (12, 12)? (a) (22, 12) (b) (11, 6) (c) (6, 11) (d) (1, 6)
  13. 13.What is the distance between the points (9, 16) and (21, 0)? (a) 20 (b) 28 (c) 21 (d) 400
  14. 14.What is the midpoint of the line joining (5, 6) and (15, 0)? (a) (5, 3) (b) (3, 10) (c) (20, 6) (d) (10, 3)
  15. 15.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 225 (c) 16 (d) 21
  16. 16.In which quadrant does the point (8, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  17. 17.What is the distance between the points (7, 16) and (22, 8)? (a) 23 (b) 17 (c) 18 (d) 289
  18. 18.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  19. 19.In which quadrant does the point (−5, −3) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  20. 20.In which quadrant does the point (−1, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  21. 21.What is the midpoint of the line joining (9, 7) and (15, 1)? (a) (24, 8) (b) (12, 4) (c) (3, 3) (d) (4, 12)
  22. 22.What is the distance between the points (6, 4) and (13, 28)? (a) 25 (b) 625 (c) 26 (d) 31
  23. 23.What is the midpoint of the line joining (4, 13) and (14, 9)? (a) (5, 2) (b) (18, 22) (c) (11, 9) (d) (9, 11)
  24. 24.What is the midpoint of the line joining (1, 4) and (3, 0)? (a) (4, 4) (b) (2, 2) (c) (1, 2) (d) (3, 2)
  25. 25.What is the midpoint of the line joining (5, 5) and (15, 1)? (a) (20, 6) (b) (5, 2) (c) (10, 3) (d) (3, 10)
  26. 26.What is the distance between the points (5, 3) and (17, 12)? (a) 21 (b) 225 (c) 15 (d) 16
  27. 27.How far is the point (24, 7) from the origin (0, 0)? (a) 31 (b) 25 (c) 26 (d) 625
  28. 28.In which quadrant does the point (−8, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  29. 29.In which quadrant does the point (−9, −7) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  30. 30.What is the midpoint of the line joining (3, 1) and (11, 9)? (a) (7, 5) (b) (4, 4) (c) (14, 10) (d) (5, 7)
  31. 31.In which quadrant does the point (7, −9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  32. 32.In which quadrant does the point (2, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  33. 33.What is the distance between the points (7, 8) and (15, 14)? (a) 11 (b) 100 (c) 14 (d) 10
  34. 34.What is the midpoint of the line joining (3, 4) and (7, 14)? (a) (2, 5) (b) (5, 9) (c) (10, 18) (d) (9, 5)
  35. 35.What is the distance between the points (2, 14) and (8, 6)? (a) 10 (b) 11 (c) 14 (d) 100
  36. 36.What is the midpoint of the line joining (1, 9) and (13, 15)? (a) (7, 12) (b) (12, 7) (c) (6, 3) (d) (14, 24)
  37. 37.What is the midpoint of the line joining (0, 21) and (4, 9)? (a) (2, 6) (b) (15, 2) (c) (4, 30) (d) (2, 15)
  38. 38.What is the distance between the points (5, 6) and (10, 18)? (a) 169 (b) 13 (c) 17 (d) 14
  39. 39.What is the distance between the points (4, 12) and (16, 7)? (a) 17 (b) 169 (c) 13 (d) 14
  40. 40.In which quadrant does the point (−3, −3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant

Answer key

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

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