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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 263 · 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 (−4, −5) lie? (a) Second quadrant (b) First quadrant (c) Third quadrant (d) Fourth quadrant
  2. 2.How far is the point (9, 12) from the origin (0, 0)? (a) 225 (b) 16 (c) 21 (d) 15
  3. 3.In which quadrant does the point (1, 8) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  4. 4.How far is the point (3, 4) from the origin (0, 0)? (a) 6 (b) 7 (c) 5 (d) 25
  5. 5.How far is the point (15, 8) from the origin (0, 0)? (a) 23 (b) 18 (c) 17 (d) 289
  6. 6.What is the midpoint of the line joining (0, 8) and (12, 4)? (a) (12, 12) (b) (6, 2) (c) (7, 6) (d) (6, 6)
  7. 7.In which quadrant does the point (6, 8) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  8. 8.What is the distance between the points (9, 8) and (12, 4)? (a) 25 (b) 5 (c) 7 (d) 6
  9. 9.What is the midpoint of the line joining (7, 9) and (9, 11)? (a) (1, 1) (b) (16, 20) (c) (10, 8) (d) (8, 10)
  10. 10.What is the midpoint of the line joining (2, 13) and (12, 5)? (a) (7, 9) (b) (5, 4) (c) (14, 18) (d) (9, 7)
  11. 11.What is the midpoint of the line joining (7, 12) and (9, 8)? (a) (8, 10) (b) (16, 20) (c) (10, 8) (d) (1, 2)
  12. 12.How far is the point (8, 6) from the origin (0, 0)? (a) 10 (b) 14 (c) 100 (d) 11
  13. 13.In which quadrant does the point (−6, 1) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  14. 14.In which quadrant does the point (−2, 5) lie? (a) Third quadrant (b) Fourth quadrant (c) First quadrant (d) Second quadrant
  15. 15.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 31 (c) 25 (d) 26
  16. 16.What is the midpoint of the line joining (2, 13) and (4, 1)? (a) (1, 6) (b) (7, 3) (c) (3, 7) (d) (6, 14)
  17. 17.What is the distance between the points (2, 5) and (14, 10)? (a) 17 (b) 14 (c) 13 (d) 169
  18. 18.What is the distance between the points (2, 8) and (10, 2)? (a) 100 (b) 11 (c) 14 (d) 10
  19. 19.In which quadrant does the point (2, −5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  20. 20.What is the distance between the points (2, 15) and (26, 8)? (a) 25 (b) 625 (c) 31 (d) 26
  21. 21.How far is the point (5, 12) from the origin (0, 0)? (a) 169 (b) 17 (c) 13 (d) 14
  22. 22.What is the distance between the points (2, 13) and (5, 9)? (a) 6 (b) 5 (c) 25 (d) 7
  23. 23.What is the distance between the points (3, 17) and (19, 5)? (a) 28 (b) 21 (c) 400 (d) 20
  24. 24.What is the distance between the points (6, 7) and (9, 11)? (a) 7 (b) 6 (c) 5 (d) 25
  25. 25.How far is the point (6, 8) from the origin (0, 0)? (a) 11 (b) 100 (c) 10 (d) 14
  26. 26.What is the midpoint of the line joining (0, 8) and (10, 12)? (a) (10, 5) (b) (10, 20) (c) (5, 10) (d) (5, 2)
  27. 27.In which quadrant does the point (8, −7) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  28. 28.In which quadrant does the point (−7, −9) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  29. 29.What is the distance between the points (9, 12) and (17, 6)? (a) 14 (b) 100 (c) 11 (d) 10
  30. 30.What is the distance between the points (0, 29) and (7, 5)? (a) 31 (b) 625 (c) 26 (d) 25
  31. 31.What is the distance between the points (1, 24) and (9, 9)? (a) 18 (b) 289 (c) 17 (d) 23
  32. 32.In which quadrant does the point (5, 6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  33. 33.What is the distance between the points (1, 3) and (16, 11)? (a) 18 (b) 289 (c) 23 (d) 17
  34. 34.In which quadrant does the point (5, 4) lie? (a) Fourth quadrant (b) Third quadrant (c) Second quadrant (d) First quadrant
  35. 35.What is the midpoint of the line joining (0, 17) and (4, 9)? (a) (2, 4) (b) (4, 26) (c) (13, 2) (d) (2, 13)
  36. 36.In which quadrant does the point (6, 5) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  37. 37.What is the distance between the points (1, 2) and (9, 17)? (a) 17 (b) 18 (c) 23 (d) 289
  38. 38.How far is the point (16, 12) from the origin (0, 0)? (a) 28 (b) 21 (c) 400 (d) 20
  39. 39.In which quadrant does the point (−8, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  40. 40.In which quadrant does the point (5, 1) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant

Answer key

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

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