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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 259 · 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 (12, 16) from the origin (0, 0)? (a) 28 (b) 400 (c) 20 (d) 21
  2. 2.In which quadrant does the point (−2, −4) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  3. 3.In which quadrant does the point (−8, −1) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  4. 4.What is the midpoint of the line joining (2, 3) and (6, 11)? (a) (7, 4) (b) (2, 4) (c) (8, 14) (d) (4, 7)
  5. 5.What is the distance between the points (0, 13) and (12, 4)? (a) 16 (b) 15 (c) 225 (d) 21
  6. 6.How far is the point (9, 12) from the origin (0, 0)? (a) 15 (b) 16 (c) 21 (d) 225
  7. 7.In which quadrant does the point (7, 4) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  8. 8.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  9. 9.In which quadrant does the point (−2, −2) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  10. 10.How far is the point (16, 12) from the origin (0, 0)? (a) 400 (b) 20 (c) 21 (d) 28
  11. 11.How far is the point (4, 3) from the origin (0, 0)? (a) 25 (b) 7 (c) 6 (d) 5
  12. 12.What is the midpoint of the line joining (10, 8) and (22, 6)? (a) (16, 7) (b) (7, 16) (c) (6, 1) (d) (32, 14)
  13. 13.What is the distance between the points (4, 13) and (19, 5)? (a) 289 (b) 18 (c) 23 (d) 17
  14. 14.What is the distance between the points (8, 4) and (12, 1)? (a) 6 (b) 7 (c) 5 (d) 25
  15. 15.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  16. 16.How far is the point (12, 5) from the origin (0, 0)? (a) 17 (b) 169 (c) 13 (d) 14
  17. 17.In which quadrant does the point (7, −4) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  18. 18.What is the distance between the points (7, 8) and (10, 4)? (a) 7 (b) 6 (c) 25 (d) 5
  19. 19.In which quadrant does the point (5, −1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  20. 20.What is the distance between the points (3, 25) and (10, 1)? (a) 25 (b) 625 (c) 26 (d) 31
  21. 21.In which quadrant does the point (1, 1) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  22. 22.What is the distance between the points (0, 1) and (12, 6)? (a) 17 (b) 169 (c) 14 (d) 13
  23. 23.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 31 (d) 25
  24. 24.What is the distance between the points (3, 1) and (18, 9)? (a) 289 (b) 18 (c) 17 (d) 23
  25. 25.What is the midpoint of the line joining (8, 4) and (14, 16)? (a) (22, 20) (b) (3, 6) (c) (10, 11) (d) (11, 10)
  26. 26.What is the distance between the points (7, 3) and (13, 11)? (a) 100 (b) 10 (c) 14 (d) 11
  27. 27.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14
  28. 28.In which quadrant does the point (−9, −2) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  29. 29.What is the distance between the points (7, 4) and (11, 7)? (a) 5 (b) 25 (c) 6 (d) 7
  30. 30.In which quadrant does the point (4, 3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  31. 31.In which quadrant does the point (−7, −6) lie? (a) First quadrant (b) Fourth quadrant (c) Second quadrant (d) Third quadrant
  32. 32.What is the distance between the points (9, 0) and (33, 7)? (a) 31 (b) 625 (c) 25 (d) 26
  33. 33.What is the midpoint of the line joining (3, 4) and (13, 12)? (a) (9, 8) (b) (16, 16) (c) (5, 4) (d) (8, 8)
  34. 34.In which quadrant does the point (4, 1) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  35. 35.How far is the point (5, 12) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
  36. 36.In which quadrant does the point (4, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  37. 37.In which quadrant does the point (1, 8) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  38. 38.What is the distance between the points (5, 15) and (13, 0)? (a) 18 (b) 289 (c) 23 (d) 17
  39. 39.What is the distance between the points (1, 1) and (9, 16)? (a) 17 (b) 23 (c) 18 (d) 289
  40. 40.What is the distance between the points (3, 5) and (8, 17)? (a) 169 (b) 17 (c) 14 (d) 13

Answer key

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

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