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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 550 · 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 (3, 6) and (19, 18)? (a) 400 (b) 21 (c) 28 (d) 20
  2. 2.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  3. 3.In which quadrant does the point (−3, 9) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  4. 4.What is the distance between the points (2, 12) and (18, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  5. 5.What is the midpoint of the line joining (4, 7) and (14, 19)? (a) (18, 26) (b) (5, 6) (c) (9, 13) (d) (13, 9)
  6. 6.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  7. 7.In which quadrant does the point (2, −3) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  8. 8.What is the midpoint of the line joining (5, 20) and (11, 8)? (a) (14, 8) (b) (8, 14) (c) (3, 6) (d) (16, 28)
  9. 9.What is the distance between the points (7, 17) and (22, 9)? (a) 289 (b) 23 (c) 18 (d) 17
  10. 10.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  11. 11.What is the distance between the points (0, 1) and (5, 13)? (a) 13 (b) 14 (c) 169 (d) 17
  12. 12.What is the midpoint of the line joining (4, 7) and (8, 19)? (a) (12, 26) (b) (2, 6) (c) (6, 13) (d) (13, 6)
  13. 13.What is the distance between the points (9, 1) and (12, 5)? (a) 25 (b) 6 (c) 5 (d) 7
  14. 14.What is the midpoint of the line joining (9, 17) and (13, 9)? (a) (13, 11) (b) (22, 26) (c) (11, 13) (d) (2, 4)
  15. 15.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
  16. 16.In which quadrant does the point (2, −2) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  17. 17.What is the distance between the points (2, 3) and (17, 11)? (a) 289 (b) 23 (c) 18 (d) 17
  18. 18.In which quadrant does the point (5, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  19. 19.What is the distance between the points (8, 7) and (14, 15)? (a) 11 (b) 14 (c) 100 (d) 10
  20. 20.What is the midpoint of the line joining (6, 10) and (18, 2)? (a) (12, 6) (b) (6, 4) (c) (6, 12) (d) (24, 12)
  21. 21.In which quadrant does the point (−9, 8) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  22. 22.How far is the point (3, 4) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  23. 23.In which quadrant does the point (−7, 2) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  24. 24.In which quadrant does the point (−2, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  25. 25.In which quadrant does the point (−3, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  26. 26.What is the distance between the points (5, 12) and (8, 8)? (a) 25 (b) 7 (c) 6 (d) 5
  27. 27.What is the distance between the points (2, 12) and (7, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  28. 28.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 21 (d) 15
  29. 29.What is the distance between the points (8, 11) and (14, 3)? (a) 11 (b) 10 (c) 14 (d) 100
  30. 30.What is the midpoint of the line joining (6, 8) and (18, 10)? (a) (6, 1) (b) (9, 12) (c) (24, 18) (d) (12, 9)
  31. 31.What is the distance between the points (6, 12) and (15, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  32. 32.What is the midpoint of the line joining (10, 3) and (18, 7)? (a) (5, 14) (b) (4, 2) (c) (28, 10) (d) (14, 5)
  33. 33.What is the distance between the points (2, 1) and (26, 8)? (a) 26 (b) 31 (c) 25 (d) 625
  34. 34.What is the distance between the points (4, 32) and (11, 8)? (a) 26 (b) 31 (c) 625 (d) 25
  35. 35.What is the distance between the points (1, 25) and (13, 9)? (a) 28 (b) 20 (c) 400 (d) 21
  36. 36.What is the distance between the points (9, 1) and (25, 13)? (a) 400 (b) 20 (c) 21 (d) 28
  37. 37.What is the distance between the points (6, 7) and (12, 15)? (a) 100 (b) 14 (c) 10 (d) 11
  38. 38.What is the distance between the points (7, 11) and (11, 8)? (a) 25 (b) 5 (c) 7 (d) 6
  39. 39.What is the midpoint of the line joining (3, 9) and (9, 21)? (a) (3, 6) (b) (6, 15) (c) (15, 6) (d) (12, 30)
  40. 40.In which quadrant does the point (9, −6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant

Answer key

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

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