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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 90 · 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.What is the distance between the points (7, 7) and (13, 15)? (a) 100 (b) 10 (c) 14 (d) 11
  2. 2.What is the distance between the points (6, 5) and (15, 17)? (a) 225 (b) 15 (c) 21 (d) 16
  3. 3.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 15 (c) 21 (d) 16
  4. 4.What is the midpoint of the line joining (4, 9) and (16, 5)? (a) (20, 14) (b) (10, 7) (c) (6, 2) (d) (7, 10)
  5. 5.In which quadrant does the point (3, −1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  6. 6.In which quadrant does the point (−1, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  7. 7.In which quadrant does the point (3, 6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  8. 8.What is the distance between the points (3, 10) and (27, 3)? (a) 26 (b) 25 (c) 31 (d) 625
  9. 9.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  10. 10.What is the distance between the points (4, 14) and (19, 6)? (a) 289 (b) 17 (c) 18 (d) 23
  11. 11.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 21 (c) 20 (d) 28
  12. 12.What is the distance between the points (5, 9) and (13, 15)? (a) 14 (b) 100 (c) 11 (d) 10
  13. 13.In which quadrant does the point (−1, 2) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  14. 14.What is the midpoint of the line joining (1, 8) and (3, 18)? (a) (1, 5) (b) (4, 26) (c) (13, 2) (d) (2, 13)
  15. 15.What is the distance between the points (2, 1) and (17, 9)? (a) 289 (b) 23 (c) 18 (d) 17
  16. 16.What is the midpoint of the line joining (0, 12) and (8, 10)? (a) (11, 4) (b) (4, 11) (c) (8, 22) (d) (4, 1)
  17. 17.How far is the point (8, 15) from the origin (0, 0)? (a) 17 (b) 23 (c) 18 (d) 289
  18. 18.How far is the point (12, 16) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  19. 19.What is the distance between the points (0, 6) and (8, 21)? (a) 18 (b) 23 (c) 17 (d) 289
  20. 20.What is the midpoint of the line joining (2, 18) and (6, 6)? (a) (4, 12) (b) (12, 4) (c) (8, 24) (d) (2, 6)
  21. 21.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 25 (c) 6 (d) 5
  22. 22.What is the distance between the points (5, 21) and (14, 9)? (a) 225 (b) 21 (c) 15 (d) 16
  23. 23.What is the midpoint of the line joining (9, 13) and (17, 5)? (a) (26, 18) (b) (9, 13) (c) (13, 9) (d) (4, 4)
  24. 24.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  25. 25.What is the midpoint of the line joining (5, 7) and (9, 17)? (a) (2, 5) (b) (12, 7) (c) (7, 12) (d) (14, 24)
  26. 26.What is the midpoint of the line joining (6, 2) and (10, 10)? (a) (2, 4) (b) (8, 6) (c) (16, 12) (d) (6, 8)
  27. 27.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 14 (d) 13
  28. 28.In which quadrant does the point (−2, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  29. 29.What is the midpoint of the line joining (9, 7) and (19, 17)? (a) (5, 5) (b) (28, 24) (c) (12, 14) (d) (14, 12)
  30. 30.What is the distance between the points (3, 4) and (18, 12)? (a) 23 (b) 289 (c) 18 (d) 17
  31. 31.In which quadrant does the point (−8, −1) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  32. 32.In which quadrant does the point (9, −6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  33. 33.In which quadrant does the point (1, −4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  34. 34.What is the distance between the points (0, 2) and (12, 11)? (a) 225 (b) 21 (c) 16 (d) 15
  35. 35.What is the midpoint of the line joining (2, 7) and (14, 1)? (a) (4, 8) (b) (16, 8) (c) (6, 3) (d) (8, 4)
  36. 36.In which quadrant does the point (7, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  37. 37.What is the midpoint of the line joining (9, 7) and (13, 15)? (a) (2, 4) (b) (22, 22) (c) (11, 11) (d) (12, 11)
  38. 38.What is the distance between the points (8, 8) and (20, 17)? (a) 15 (b) 21 (c) 225 (d) 16
  39. 39.In which quadrant does the point (7, −6) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  40. 40.What is the distance between the points (3, 6) and (7, 3)? (a) 25 (b) 7 (c) 5 (d) 6

Answer key

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

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