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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 515 · 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) 21 (b) 20 (c) 400 (d) 28
  2. 2.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  3. 3.In which quadrant does the point (5, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  4. 4.What is the midpoint of the line joining (1, 19) and (3, 7)? (a) (2, 13) (b) (13, 2) (c) (4, 26) (d) (1, 6)
  5. 5.What is the distance between the points (3, 8) and (9, 16)? (a) 10 (b) 14 (c) 100 (d) 11
  6. 6.What is the midpoint of the line joining (4, 11) and (16, 3)? (a) (6, 4) (b) (7, 10) (c) (20, 14) (d) (10, 7)
  7. 7.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 17 (c) 13 (d) 169
  8. 8.What is the distance between the points (4, 12) and (16, 7)? (a) 17 (b) 14 (c) 13 (d) 169
  9. 9.In which quadrant does the point (6, −4) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  10. 10.What is the midpoint of the line joining (0, 2) and (10, 12)? (a) (5, 5) (b) (10, 14) (c) (5, 7) (d) (7, 5)
  11. 11.What is the midpoint of the line joining (10, 9) and (20, 7)? (a) (8, 15) (b) (15, 8) (c) (30, 16) (d) (5, 1)
  12. 12.How far is the point (7, 24) from the origin (0, 0)? (a) 25 (b) 31 (c) 625 (d) 26
  13. 13.What is the distance between the points (2, 1) and (7, 13)? (a) 13 (b) 17 (c) 169 (d) 14
  14. 14.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  15. 15.What is the distance between the points (4, 8) and (16, 24)? (a) 400 (b) 21 (c) 28 (d) 20
  16. 16.What is the midpoint of the line joining (10, 11) and (12, 1)? (a) (1, 5) (b) (11, 6) (c) (6, 11) (d) (22, 12)
  17. 17.In which quadrant does the point (8, −4) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  18. 18.What is the distance between the points (4, 12) and (9, 0)? (a) 169 (b) 13 (c) 17 (d) 14
  19. 19.What is the midpoint of the line joining (0, 0) and (8, 12)? (a) (4, 6) (b) (6, 4) (c) (8, 12) (d) (5, 6)
  20. 20.What is the distance between the points (6, 14) and (22, 2)? (a) 400 (b) 28 (c) 21 (d) 20
  21. 21.In which quadrant does the point (−4, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  22. 22.What is the distance between the points (4, 6) and (12, 12)? (a) 100 (b) 14 (c) 11 (d) 10
  23. 23.In which quadrant does the point (−1, 9) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  24. 24.In which quadrant does the point (−4, 1) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  25. 25.What is the midpoint of the line joining (7, 6) and (19, 0)? (a) (13, 3) (b) (26, 6) (c) (6, 3) (d) (3, 13)
  26. 26.What is the midpoint of the line joining (4, 6) and (16, 18)? (a) (6, 6) (b) (12, 10) (c) (10, 12) (d) (20, 24)
  27. 27.What is the midpoint of the line joining (3, 21) and (15, 9)? (a) (18, 30) (b) (9, 15) (c) (6, 6) (d) (15, 9)
  28. 28.In which quadrant does the point (6, −8) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  29. 29.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 25 (c) 5 (d) 6
  30. 30.What is the midpoint of the line joining (5, 2) and (13, 0)? (a) (1, 9) (b) (9, 1) (c) (18, 2) (d) (4, 1)
  31. 31.What is the midpoint of the line joining (0, 10) and (6, 16)? (a) (13, 3) (b) (3, 3) (c) (6, 26) (d) (3, 13)
  32. 32.What is the midpoint of the line joining (6, 3) and (16, 1)? (a) (2, 11) (b) (5, 1) (c) (11, 2) (d) (22, 4)
  33. 33.In which quadrant does the point (4, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  34. 34.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 17 (c) 289 (d) 18
  35. 35.What is the midpoint of the line joining (6, 8) and (10, 20)? (a) (2, 6) (b) (14, 8) (c) (8, 14) (d) (16, 28)
  36. 36.In which quadrant does the point (−3, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  37. 37.What is the distance between the points (7, 12) and (22, 4)? (a) 23 (b) 18 (c) 17 (d) 289
  38. 38.In which quadrant does the point (−4, −3) lie? (a) Second quadrant (b) Third quadrant (c) Fourth quadrant (d) First quadrant
  39. 39.In which quadrant does the point (1, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  40. 40.What is the distance between the points (2, 4) and (9, 28)? (a) 625 (b) 25 (c) 26 (d) 31

Answer key

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

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