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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 96 · 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 (7, 24) from the origin (0, 0)? (a) 25 (b) 26 (c) 625 (d) 31
  2. 2.In which quadrant does the point (9, 3) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  3. 3.In which quadrant does the point (−1, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  4. 4.What is the distance between the points (3, 9) and (15, 18)? (a) 225 (b) 15 (c) 21 (d) 16
  5. 5.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  6. 6.How far is the point (12, 9) from the origin (0, 0)? (a) 21 (b) 16 (c) 15 (d) 225
  7. 7.What is the distance between the points (2, 1) and (14, 6)? (a) 17 (b) 13 (c) 14 (d) 169
  8. 8.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 17 (c) 23 (d) 289
  9. 9.What is the distance between the points (0, 13) and (6, 5)? (a) 14 (b) 100 (c) 11 (d) 10
  10. 10.What is the distance between the points (4, 5) and (12, 11)? (a) 11 (b) 14 (c) 10 (d) 100
  11. 11.What is the distance between the points (9, 2) and (18, 14)? (a) 15 (b) 16 (c) 225 (d) 21
  12. 12.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 13 (d) 17
  13. 13.In which quadrant does the point (−1, 8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  14. 14.In which quadrant does the point (3, 2) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  15. 15.What is the distance between the points (4, 9) and (10, 1)? (a) 10 (b) 14 (c) 11 (d) 100
  16. 16.In which quadrant does the point (6, −6) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  17. 17.What is the distance between the points (5, 3) and (9, 6)? (a) 7 (b) 25 (c) 6 (d) 5
  18. 18.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 11 (c) 100 (d) 10
  19. 19.In which quadrant does the point (−3, −9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  20. 20.What is the distance between the points (2, 3) and (14, 19)? (a) 21 (b) 20 (c) 400 (d) 28
  21. 21.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 14 (c) 169 (d) 13
  22. 22.How far is the point (4, 3) from the origin (0, 0)? (a) 6 (b) 25 (c) 7 (d) 5
  23. 23.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  24. 24.What is the distance between the points (8, 17) and (17, 5)? (a) 16 (b) 225 (c) 21 (d) 15
  25. 25.In which quadrant does the point (−7, 7) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  26. 26.What is the distance between the points (6, 33) and (13, 9)? (a) 625 (b) 31 (c) 26 (d) 25
  27. 27.What is the midpoint of the line joining (7, 9) and (11, 1)? (a) (9, 5) (b) (18, 10) (c) (5, 9) (d) (2, 4)
  28. 28.What is the distance between the points (4, 10) and (7, 6)? (a) 7 (b) 25 (c) 6 (d) 5
  29. 29.What is the distance between the points (7, 7) and (11, 4)? (a) 7 (b) 6 (c) 25 (d) 5
  30. 30.What is the distance between the points (0, 9) and (6, 17)? (a) 100 (b) 11 (c) 10 (d) 14
  31. 31.What is the distance between the points (0, 20) and (8, 5)? (a) 23 (b) 289 (c) 17 (d) 18
  32. 32.What is the distance between the points (2, 0) and (17, 8)? (a) 23 (b) 289 (c) 18 (d) 17
  33. 33.In which quadrant does the point (−3, −6) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  34. 34.What is the midpoint of the line joining (0, 20) and (10, 8)? (a) (5, 14) (b) (14, 5) (c) (5, 6) (d) (10, 28)
  35. 35.What is the distance between the points (5, 5) and (11, 13)? (a) 100 (b) 11 (c) 10 (d) 14
  36. 36.How far is the point (3, 4) from the origin (0, 0)? (a) 7 (b) 5 (c) 25 (d) 6
  37. 37.What is the distance between the points (4, 11) and (19, 3)? (a) 17 (b) 289 (c) 18 (d) 23
  38. 38.What is the midpoint of the line joining (8, 4) and (18, 12)? (a) (8, 13) (b) (5, 4) (c) (26, 16) (d) (13, 8)
  39. 39.In which quadrant does the point (−4, 7) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  40. 40.What is the distance between the points (6, 9) and (9, 13)? (a) 7 (b) 6 (c) 5 (d) 25

Answer key

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

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