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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 309 · 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 (12, 16) from the origin (0, 0)? (a) 400 (b) 28 (c) 21 (d) 20
  2. 2.In which quadrant does the point (2, 6) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  3. 3.What is the distance between the points (5, 8) and (13, 2)? (a) 10 (b) 100 (c) 14 (d) 11
  4. 4.What is the midpoint of the line joining (4, 4) and (14, 8)? (a) (5, 2) (b) (6, 9) (c) (9, 6) (d) (18, 12)
  5. 5.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 25 (c) 7 (d) 6
  6. 6.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 10 (d) 100
  7. 7.What is the midpoint of the line joining (4, 6) and (8, 10)? (a) (2, 2) (b) (8, 6) (c) (6, 8) (d) (12, 16)
  8. 8.How far is the point (5, 12) from the origin (0, 0)? (a) 17 (b) 14 (c) 13 (d) 169
  9. 9.What is the distance between the points (0, 12) and (16, 0)? (a) 28 (b) 400 (c) 21 (d) 20
  10. 10.What is the distance between the points (1, 9) and (7, 17)? (a) 11 (b) 100 (c) 10 (d) 14
  11. 11.What is the midpoint of the line joining (6, 4) and (10, 0)? (a) (16, 4) (b) (2, 2) (c) (8, 2) (d) (2, 8)
  12. 12.What is the distance between the points (1, 9) and (9, 15)? (a) 11 (b) 10 (c) 100 (d) 14
  13. 13.What is the distance between the points (0, 2) and (6, 10)? (a) 11 (b) 10 (c) 14 (d) 100
  14. 14.What is the distance between the points (8, 5) and (16, 11)? (a) 14 (b) 100 (c) 11 (d) 10
  15. 15.What is the distance between the points (3, 6) and (27, 13)? (a) 26 (b) 625 (c) 31 (d) 25
  16. 16.What is the distance between the points (6, 3) and (21, 11)? (a) 23 (b) 18 (c) 289 (d) 17
  17. 17.What is the midpoint of the line joining (9, 7) and (11, 17)? (a) (12, 10) (b) (1, 5) (c) (20, 24) (d) (10, 12)
  18. 18.What is the distance between the points (3, 3) and (11, 18)? (a) 23 (b) 289 (c) 17 (d) 18
  19. 19.In which quadrant does the point (−1, −8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  20. 20.What is the midpoint of the line joining (2, 1) and (6, 7)? (a) (2, 3) (b) (5, 4) (c) (4, 4) (d) (8, 8)
  21. 21.What is the distance between the points (4, 12) and (13, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  22. 22.What is the midpoint of the line joining (10, 4) and (12, 6)? (a) (1, 1) (b) (5, 11) (c) (22, 10) (d) (11, 5)
  23. 23.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 25 (c) 26 (d) 31
  24. 24.What is the distance between the points (4, 6) and (8, 9)? (a) 25 (b) 7 (c) 6 (d) 5
  25. 25.What is the distance between the points (1, 14) and (13, 9)? (a) 17 (b) 13 (c) 14 (d) 169
  26. 26.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 18 (d) 17
  27. 27.What is the midpoint of the line joining (7, 3) and (19, 5)? (a) (26, 8) (b) (13, 4) (c) (6, 1) (d) (4, 13)
  28. 28.What is the distance between the points (7, 2) and (13, 10)? (a) 100 (b) 11 (c) 14 (d) 10
  29. 29.What is the distance between the points (2, 5) and (17, 13)? (a) 18 (b) 17 (c) 23 (d) 289
  30. 30.In which quadrant does the point (−9, −9) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  31. 31.What is the distance between the points (9, 5) and (14, 17)? (a) 13 (b) 14 (c) 17 (d) 169
  32. 32.What is the midpoint of the line joining (0, 0) and (4, 4)? (a) (3, 2) (b) (2, 2) (c) (2, 3) (d) (4, 4)
  33. 33.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  34. 34.How far is the point (12, 5) from the origin (0, 0)? (a) 14 (b) 13 (c) 17 (d) 169
  35. 35.In which quadrant does the point (5, 9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  36. 36.What is the distance between the points (8, 1) and (20, 17)? (a) 20 (b) 21 (c) 400 (d) 28
  37. 37.In which quadrant does the point (6, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  38. 38.In which quadrant does the point (8, 5) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  39. 39.What is the midpoint of the line joining (7, 18) and (15, 10)? (a) (22, 28) (b) (14, 11) (c) (4, 4) (d) (11, 14)
  40. 40.In which quadrant does the point (6, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant

Answer key

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

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