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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 109 · 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 midpoint of the line joining (5, 14) and (7, 10)? (a) (12, 6) (b) (6, 12) (c) (1, 2) (d) (12, 24)
  2. 2.What is the distance between the points (1, 5) and (4, 1)? (a) 7 (b) 5 (c) 6 (d) 25
  3. 3.What is the midpoint of the line joining (9, 9) and (21, 1)? (a) (6, 4) (b) (5, 15) (c) (30, 10) (d) (15, 5)
  4. 4.What is the distance between the points (1, 15) and (9, 9)? (a) 14 (b) 100 (c) 10 (d) 11
  5. 5.How far is the point (7, 24) from the origin (0, 0)? (a) 31 (b) 625 (c) 26 (d) 25
  6. 6.What is the distance between the points (1, 2) and (6, 14)? (a) 169 (b) 17 (c) 14 (d) 13
  7. 7.In which quadrant does the point (−8, −1) lie? (a) Third quadrant (b) Second quadrant (c) Fourth quadrant (d) First quadrant
  8. 8.What is the distance between the points (1, 1) and (7, 9)? (a) 100 (b) 14 (c) 11 (d) 10
  9. 9.What is the midpoint of the line joining (5, 8) and (7, 18)? (a) (12, 26) (b) (6, 13) (c) (13, 6) (d) (1, 5)
  10. 10.What is the distance between the points (8, 5) and (16, 11)? (a) 14 (b) 100 (c) 10 (d) 11
  11. 11.How far is the point (12, 16) from the origin (0, 0)? (a) 21 (b) 400 (c) 28 (d) 20
  12. 12.What is the distance between the points (8, 9) and (12, 6)? (a) 25 (b) 7 (c) 5 (d) 6
  13. 13.In which quadrant does the point (−8, −8) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  14. 14.What is the midpoint of the line joining (7, 10) and (11, 2)? (a) (9, 6) (b) (6, 9) (c) (2, 4) (d) (18, 12)
  15. 15.In which quadrant does the point (9, −2) lie? (a) Fourth quadrant (b) Second quadrant (c) Third quadrant (d) First quadrant
  16. 16.What is the distance between the points (0, 2) and (8, 8)? (a) 14 (b) 100 (c) 10 (d) 11
  17. 17.In which quadrant does the point (−5, −9) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  18. 18.In which quadrant does the point (−7, −9) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  19. 19.How far is the point (8, 15) from the origin (0, 0)? (a) 289 (b) 23 (c) 17 (d) 18
  20. 20.What is the distance between the points (2, 13) and (18, 1)? (a) 20 (b) 400 (c) 21 (d) 28
  21. 21.In which quadrant does the point (−6, 5) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  22. 22.In which quadrant does the point (7, 1) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  23. 23.In which quadrant does the point (−7, 3) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  24. 24.In which quadrant does the point (−5, −6) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  25. 25.What is the distance between the points (0, 8) and (6, 0)? (a) 14 (b) 11 (c) 10 (d) 100
  26. 26.What is the distance between the points (7, 8) and (15, 14)? (a) 11 (b) 100 (c) 10 (d) 14
  27. 27.In which quadrant does the point (−7, 9) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  28. 28.What is the midpoint of the line joining (4, 20) and (8, 10)? (a) (15, 6) (b) (12, 30) (c) (2, 5) (d) (6, 15)
  29. 29.What is the midpoint of the line joining (10, 8) and (22, 0)? (a) (32, 8) (b) (6, 4) (c) (16, 4) (d) (4, 16)
  30. 30.In which quadrant does the point (−3, 2) lie? (a) Second quadrant (b) Third quadrant (c) First quadrant (d) Fourth quadrant
  31. 31.In which quadrant does the point (9, 6) lie? (a) Fourth quadrant (b) First quadrant (c) Third quadrant (d) Second quadrant
  32. 32.What is the midpoint of the line joining (5, 17) and (15, 7)? (a) (12, 10) (b) (5, 5) (c) (20, 24) (d) (10, 12)
  33. 33.What is the distance between the points (8, 13) and (16, 7)? (a) 11 (b) 14 (c) 100 (d) 10
  34. 34.In which quadrant does the point (−1, 8) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  35. 35.What is the distance between the points (5, 14) and (10, 2)? (a) 169 (b) 13 (c) 17 (d) 14
  36. 36.What is the distance between the points (0, 7) and (15, 15)? (a) 289 (b) 23 (c) 17 (d) 18
  37. 37.What is the distance between the points (8, 17) and (20, 1)? (a) 400 (b) 20 (c) 28 (d) 21
  38. 38.What is the distance between the points (6, 12) and (18, 3)? (a) 21 (b) 225 (c) 16 (d) 15
  39. 39.What is the distance between the points (8, 8) and (14, 0)? (a) 100 (b) 14 (c) 10 (d) 11
  40. 40.In which quadrant does the point (−1, −3) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant

Answer key

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

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