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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 171 · 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 (1, 7) and (25, 0)? (a) 625 (b) 25 (c) 26 (d) 31
  2. 2.What is the midpoint of the line joining (0, 4) and (2, 12)? (a) (1, 8) (b) (1, 4) (c) (2, 16) (d) (8, 1)
  3. 3.What is the distance between the points (1, 9) and (13, 14)? (a) 169 (b) 14 (c) 17 (d) 13
  4. 4.In which quadrant does the point (−1, 4) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  5. 5.In which quadrant does the point (−8, −9) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  6. 6.What is the midpoint of the line joining (6, 10) and (18, 22)? (a) (24, 32) (b) (6, 6) (c) (12, 16) (d) (16, 12)
  7. 7.In which quadrant does the point (−1, 1) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  8. 8.What is the distance between the points (7, 14) and (12, 2)? (a) 169 (b) 13 (c) 14 (d) 17
  9. 9.In which quadrant does the point (−3, −7) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  10. 10.How far is the point (4, 3) from the origin (0, 0)? (a) 7 (b) 6 (c) 25 (d) 5
  11. 11.What is the distance between the points (2, 3) and (6, 0)? (a) 25 (b) 5 (c) 6 (d) 7
  12. 12.In which quadrant does the point (2, 9) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  13. 13.What is the midpoint of the line joining (8, 0) and (20, 12)? (a) (6, 6) (b) (6, 14) (c) (28, 12) (d) (14, 6)
  14. 14.How far is the point (12, 9) from the origin (0, 0)? (a) 16 (b) 225 (c) 15 (d) 21
  15. 15.How far is the point (8, 15) from the origin (0, 0)? (a) 23 (b) 289 (c) 18 (d) 17
  16. 16.In which quadrant does the point (1, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  17. 17.How far is the point (6, 8) from the origin (0, 0)? (a) 14 (b) 10 (c) 11 (d) 100
  18. 18.What is the distance between the points (3, 25) and (10, 1)? (a) 625 (b) 26 (c) 25 (d) 31
  19. 19.What is the midpoint of the line joining (10, 1) and (12, 13)? (a) (7, 11) (b) (22, 14) (c) (11, 7) (d) (1, 6)
  20. 20.In which quadrant does the point (4, 6) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  21. 21.What is the distance between the points (4, 26) and (11, 2)? (a) 25 (b) 26 (c) 625 (d) 31
  22. 22.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 625 (c) 25 (d) 31
  23. 23.What is the distance between the points (9, 2) and (17, 8)? (a) 100 (b) 14 (c) 11 (d) 10
  24. 24.What is the midpoint of the line joining (0, 4) and (4, 2)? (a) (3, 2) (b) (4, 6) (c) (2, 3) (d) (2, 1)
  25. 25.How far is the point (3, 4) from the origin (0, 0)? (a) 25 (b) 6 (c) 5 (d) 7
  26. 26.In which quadrant does the point (−8, −3) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  27. 27.In which quadrant does the point (−3, −4) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  28. 28.What is the distance between the points (7, 6) and (11, 3)? (a) 5 (b) 7 (c) 25 (d) 6
  29. 29.How far is the point (12, 5) from the origin (0, 0)? (a) 169 (b) 14 (c) 17 (d) 13
  30. 30.What is the distance between the points (3, 5) and (6, 1)? (a) 7 (b) 6 (c) 25 (d) 5
  31. 31.In which quadrant does the point (−2, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  32. 32.What is the distance between the points (6, 6) and (14, 12)? (a) 10 (b) 100 (c) 11 (d) 14
  33. 33.In which quadrant does the point (−2, 4) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  34. 34.In which quadrant does the point (−4, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  35. 35.What is the distance between the points (6, 8) and (14, 23)? (a) 23 (b) 289 (c) 18 (d) 17
  36. 36.What is the distance between the points (6, 18) and (11, 6)? (a) 169 (b) 17 (c) 13 (d) 14
  37. 37.What is the midpoint of the line joining (6, 1) and (18, 13)? (a) (24, 14) (b) (12, 7) (c) (7, 12) (d) (6, 6)
  38. 38.In which quadrant does the point (7, −5) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  39. 39.How far is the point (9, 12) from the origin (0, 0)? (a) 16 (b) 21 (c) 225 (d) 15
  40. 40.How far is the point (8, 6) from the origin (0, 0)? (a) 11 (b) 10 (c) 100 (d) 14

Answer key

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

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