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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 270 · 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 (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  2. 2.What is the distance between the points (3, 8) and (15, 24)? (a) 20 (b) 21 (c) 400 (d) 28
  3. 3.What is the midpoint of the line joining (9, 9) and (11, 11)? (a) (10, 10) (b) (1, 1) (c) (11, 10) (d) (20, 20)
  4. 4.What is the distance between the points (3, 2) and (15, 11)? (a) 225 (b) 16 (c) 21 (d) 15
  5. 5.What is the midpoint of the line joining (1, 5) and (13, 17)? (a) (6, 6) (b) (7, 11) (c) (14, 22) (d) (11, 7)
  6. 6.How far is the point (24, 7) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  7. 7.What is the midpoint of the line joining (7, 17) and (11, 7)? (a) (2, 5) (b) (18, 24) (c) (9, 12) (d) (12, 9)
  8. 8.What is the distance between the points (8, 2) and (16, 17)? (a) 23 (b) 18 (c) 289 (d) 17
  9. 9.In which quadrant does the point (−9, 8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  10. 10.What is the midpoint of the line joining (6, 13) and (12, 5)? (a) (18, 18) (b) (10, 9) (c) (3, 4) (d) (9, 9)
  11. 11.In which quadrant does the point (−2, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  12. 12.What is the distance between the points (6, 8) and (11, 20)? (a) 17 (b) 14 (c) 169 (d) 13
  13. 13.What is the midpoint of the line joining (9, 6) and (11, 8)? (a) (1, 1) (b) (10, 7) (c) (7, 10) (d) (20, 14)
  14. 14.What is the distance between the points (9, 17) and (21, 1)? (a) 21 (b) 400 (c) 20 (d) 28
  15. 15.What is the midpoint of the line joining (8, 7) and (20, 1)? (a) (6, 3) (b) (14, 4) (c) (4, 14) (d) (28, 8)
  16. 16.What is the midpoint of the line joining (7, 2) and (11, 12)? (a) (2, 5) (b) (18, 14) (c) (9, 7) (d) (7, 9)
  17. 17.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  18. 18.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  19. 19.What is the distance between the points (6, 1) and (12, 9)? (a) 10 (b) 100 (c) 14 (d) 11
  20. 20.In which quadrant does the point (9, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  21. 21.In which quadrant does the point (6, 2) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  22. 22.In which quadrant does the point (8, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  23. 23.In which quadrant does the point (−6, 9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  24. 24.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  25. 25.In which quadrant does the point (−1, 2) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  26. 26.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  27. 27.What is the midpoint of the line joining (1, 4) and (5, 16)? (a) (10, 3) (b) (2, 6) (c) (6, 20) (d) (3, 10)
  28. 28.What is the distance between the points (4, 5) and (19, 13)? (a) 18 (b) 289 (c) 17 (d) 23
  29. 29.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 100 (c) 11 (d) 10
  30. 30.What is the midpoint of the line joining (5, 7) and (9, 5)? (a) (7, 6) (b) (14, 12) (c) (6, 7) (d) (2, 1)
  31. 31.What is the distance between the points (9, 1) and (17, 7)? (a) 14 (b) 10 (c) 100 (d) 11
  32. 32.What is the distance between the points (5, 13) and (11, 5)? (a) 11 (b) 14 (c) 10 (d) 100
  33. 33.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 26 (c) 25 (d) 625
  34. 34.What is the distance between the points (3, 9) and (11, 24)? (a) 18 (b) 23 (c) 289 (d) 17
  35. 35.What is the distance between the points (5, 12) and (21, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  36. 36.What is the distance between the points (9, 14) and (18, 2)? (a) 21 (b) 225 (c) 16 (d) 15
  37. 37.What is the distance between the points (3, 2) and (15, 7)? (a) 14 (b) 17 (c) 13 (d) 169
  38. 38.In which quadrant does the point (−7, 7) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  39. 39.In which quadrant does the point (3, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  40. 40.In which quadrant does the point (7, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant

Answer key

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

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