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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 103 · 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 (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  2. 2.What is the distance between the points (1, 14) and (7, 6)? (a) 11 (b) 100 (c) 14 (d) 10
  3. 3.What is the midpoint of the line joining (0, 7) and (12, 5)? (a) (6, 1) (b) (6, 6) (c) (7, 6) (d) (12, 12)
  4. 4.In which quadrant does the point (5, 6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  5. 5.What is the distance between the points (9, 14) and (25, 2)? (a) 400 (b) 28 (c) 21 (d) 20
  6. 6.What is the midpoint of the line joining (4, 10) and (10, 0)? (a) (3, 5) (b) (14, 10) (c) (5, 7) (d) (7, 5)
  7. 7.What is the midpoint of the line joining (1, 0) and (7, 10)? (a) (4, 5) (b) (8, 10) (c) (3, 5) (d) (5, 4)
  8. 8.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 289 (d) 17
  9. 9.In which quadrant does the point (5, 2) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  10. 10.What is the midpoint of the line joining (1, 1) and (11, 13)? (a) (12, 14) (b) (5, 6) (c) (6, 7) (d) (7, 6)
  11. 11.In which quadrant does the point (−3, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  12. 12.In which quadrant does the point (−1, 6) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  13. 13.What is the distance between the points (9, 9) and (21, 18)? (a) 21 (b) 15 (c) 16 (d) 225
  14. 14.In which quadrant does the point (9, 3) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  15. 15.What is the midpoint of the line joining (7, 1) and (15, 7)? (a) (22, 8) (b) (4, 11) (c) (4, 3) (d) (11, 4)
  16. 16.What is the midpoint of the line joining (3, 2) and (7, 6)? (a) (10, 8) (b) (2, 2) (c) (5, 4) (d) (4, 5)
  17. 17.What is the midpoint of the line joining (4, 6) and (16, 8)? (a) (6, 1) (b) (10, 7) (c) (7, 10) (d) (20, 14)
  18. 18.In which quadrant does the point (−2, −9) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  19. 19.In which quadrant does the point (−5, 7) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  20. 20.In which quadrant does the point (1, −2) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  21. 21.What is the midpoint of the line joining (5, 10) and (9, 12)? (a) (7, 11) (b) (2, 1) (c) (11, 7) (d) (14, 22)
  22. 22.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 14 (c) 100 (d) 10
  23. 23.What is the midpoint of the line joining (3, 14) and (9, 4)? (a) (12, 18) (b) (9, 6) (c) (6, 9) (d) (3, 5)
  24. 24.What is the distance between the points (8, 8) and (12, 5)? (a) 25 (b) 6 (c) 5 (d) 7
  25. 25.What is the distance between the points (8, 23) and (20, 7)? (a) 400 (b) 20 (c) 28 (d) 21
  26. 26.What is the distance between the points (8, 12) and (16, 6)? (a) 14 (b) 10 (c) 100 (d) 11
  27. 27.What is the distance between the points (0, 7) and (5, 19)? (a) 169 (b) 14 (c) 17 (d) 13
  28. 28.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 28 (c) 400 (d) 20
  29. 29.What is the midpoint of the line joining (9, 7) and (13, 5)? (a) (11, 6) (b) (22, 12) (c) (6, 11) (d) (2, 1)
  30. 30.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 289 (d) 17
  31. 31.What is the distance between the points (1, 9) and (7, 17)? (a) 100 (b) 11 (c) 14 (d) 10
  32. 32.In which quadrant does the point (5, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  33. 33.How far is the point (9, 12) from the origin (0, 0)? (a) 21 (b) 225 (c) 15 (d) 16
  34. 34.What is the distance between the points (9, 0) and (18, 12)? (a) 15 (b) 21 (c) 225 (d) 16
  35. 35.What is the distance between the points (5, 12) and (20, 4)? (a) 17 (b) 23 (c) 18 (d) 289
  36. 36.How far is the point (7, 24) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  37. 37.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  38. 38.What is the distance between the points (5, 5) and (17, 21)? (a) 400 (b) 21 (c) 28 (d) 20
  39. 39.What is the distance between the points (9, 2) and (15, 10)? (a) 10 (b) 11 (c) 14 (d) 100
  40. 40.In which quadrant does the point (−8, −8) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant

Answer key

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

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