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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 677 · 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.In which quadrant does the point (8, −1) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  2. 2.What is the distance between the points (0, 13) and (3, 9)? (a) 7 (b) 5 (c) 25 (d) 6
  3. 3.In which quadrant does the point (1, −9) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  4. 4.What is the distance between the points (5, 8) and (17, 17)? (a) 225 (b) 16 (c) 15 (d) 21
  5. 5.What is the distance between the points (0, 9) and (12, 14)? (a) 14 (b) 17 (c) 169 (d) 13
  6. 6.How far is the point (4, 3) from the origin (0, 0)? (a) 5 (b) 7 (c) 25 (d) 6
  7. 7.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 25 (d) 26
  8. 8.What is the distance between the points (1, 3) and (13, 8)? (a) 17 (b) 169 (c) 13 (d) 14
  9. 9.What is the midpoint of the line joining (9, 7) and (17, 5)? (a) (26, 12) (b) (4, 1) (c) (13, 6) (d) (6, 13)
  10. 10.How far is the point (6, 8) from the origin (0, 0)? (a) 10 (b) 100 (c) 11 (d) 14
  11. 11.What is the distance between the points (2, 8) and (9, 32)? (a) 25 (b) 625 (c) 26 (d) 31
  12. 12.What is the distance between the points (0, 26) and (7, 2)? (a) 625 (b) 26 (c) 25 (d) 31
  13. 13.In which quadrant does the point (9, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  14. 14.In which quadrant does the point (−3, 6) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  15. 15.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 20 (c) 400 (d) 21
  16. 16.What is the distance between the points (0, 6) and (12, 15)? (a) 225 (b) 16 (c) 15 (d) 21
  17. 17.What is the midpoint of the line joining (3, 1) and (5, 7)? (a) (4, 4) (b) (1, 3) (c) (8, 8) (d) (5, 4)
  18. 18.What is the distance between the points (9, 18) and (21, 9)? (a) 15 (b) 225 (c) 16 (d) 21
  19. 19.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 20 (d) 28
  20. 20.What is the distance between the points (2, 2) and (10, 17)? (a) 289 (b) 17 (c) 23 (d) 18
  21. 21.In which quadrant does the point (−8, −8) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  22. 22.What is the midpoint of the line joining (0, 15) and (2, 5)? (a) (2, 20) (b) (1, 10) (c) (1, 5) (d) (10, 1)
  23. 23.What is the distance between the points (4, 9) and (16, 4)? (a) 14 (b) 17 (c) 13 (d) 169
  24. 24.What is the midpoint of the line joining (8, 0) and (14, 10)? (a) (5, 11) (b) (3, 5) (c) (22, 10) (d) (11, 5)
  25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 25 (c) 5 (d) 7
  26. 26.What is the midpoint of the line joining (1, 8) and (9, 2)? (a) (10, 10) (b) (4, 3) (c) (5, 5) (d) (6, 5)
  27. 27.How far is the point (8, 15) from the origin (0, 0)? (a) 18 (b) 23 (c) 17 (d) 289
  28. 28.In which quadrant does the point (−3, −8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  29. 29.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  30. 30.What is the distance between the points (2, 7) and (11, 19)? (a) 16 (b) 15 (c) 21 (d) 225
  31. 31.What is the distance between the points (3, 0) and (6, 4)? (a) 25 (b) 5 (c) 7 (d) 6
  32. 32.In which quadrant does the point (−9, 8) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  33. 33.What is the distance between the points (3, 0) and (12, 12)? (a) 225 (b) 21 (c) 15 (d) 16
  34. 34.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 15 (c) 225 (d) 21
  35. 35.In which quadrant does the point (1, −4) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  36. 36.What is the distance between the points (5, 8) and (14, 20)? (a) 16 (b) 225 (c) 15 (d) 21
  37. 37.What is the distance between the points (6, 12) and (15, 0)? (a) 15 (b) 21 (c) 225 (d) 16
  38. 38.What is the midpoint of the line joining (6, 8) and (8, 6)? (a) (7, 7) (b) (14, 14) (c) (8, 7) (d) (1, 1)
  39. 39.What is the midpoint of the line joining (7, 13) and (11, 1)? (a) (18, 14) (b) (2, 6) (c) (7, 9) (d) (9, 7)
  40. 40.How far is the point (8, 6) from the origin (0, 0)? (a) 14 (b) 11 (c) 10 (d) 100

Answer key

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

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