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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 352 · 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 (10, 3) and (18, 5)? (a) (14, 4) (b) (4, 14) (c) (4, 1) (d) (28, 8)
  2. 2.What is the distance between the points (0, 7) and (4, 4)? (a) 25 (b) 6 (c) 7 (d) 5
  3. 3.In which quadrant does the point (−4, 7) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  4. 4.What is the distance between the points (8, 9) and (11, 13)? (a) 5 (b) 7 (c) 25 (d) 6
  5. 5.What is the distance between the points (2, 7) and (5, 11)? (a) 25 (b) 5 (c) 7 (d) 6
  6. 6.How far is the point (12, 9) from the origin (0, 0)? (a) 225 (b) 21 (c) 16 (d) 15
  7. 7.In which quadrant does the point (3, 9) lie? (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant
  8. 8.What is the midpoint of the line joining (1, 2) and (13, 10)? (a) (7, 6) (b) (14, 12) (c) (6, 7) (d) (6, 4)
  9. 9.In which quadrant does the point (−2, −5) lie? (a) Fourth quadrant (b) First quadrant (c) Second quadrant (d) Third quadrant
  10. 10.What is the distance between the points (3, 0) and (15, 5)? (a) 13 (b) 14 (c) 169 (d) 17
  11. 11.What is the midpoint of the line joining (6, 2) and (14, 6)? (a) (20, 8) (b) (10, 4) (c) (4, 2) (d) (4, 10)
  12. 12.How far is the point (15, 8) from the origin (0, 0)? (a) 18 (b) 289 (c) 23 (d) 17
  13. 13.In which quadrant does the point (8, 4) lie? (a) First quadrant (b) Third quadrant (c) Second quadrant (d) Fourth quadrant
  14. 14.What is the distance between the points (0, 12) and (4, 9)? (a) 7 (b) 25 (c) 6 (d) 5
  15. 15.What is the midpoint of the line joining (4, 1) and (8, 5)? (a) (3, 6) (b) (12, 6) (c) (2, 2) (d) (6, 3)
  16. 16.What is the distance between the points (4, 12) and (13, 0)? (a) 16 (b) 15 (c) 21 (d) 225
  17. 17.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 10 (c) 14 (d) 11
  18. 18.What is the distance between the points (3, 6) and (11, 0)? (a) 100 (b) 11 (c) 10 (d) 14
  19. 19.In which quadrant does the point (8, 6) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
  20. 20.In which quadrant does the point (−7, 8) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  21. 21.What is the midpoint of the line joining (10, 10) and (20, 16)? (a) (13, 15) (b) (30, 26) (c) (5, 3) (d) (15, 13)
  22. 22.In which quadrant does the point (−9, −3) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  23. 23.What is the distance between the points (4, 2) and (11, 26)? (a) 31 (b) 625 (c) 26 (d) 25
  24. 24.In which quadrant does the point (−1, 9) lie? (a) Third quadrant (b) Second quadrant (c) First quadrant (d) Fourth quadrant
  25. 25.What is the midpoint of the line joining (0, 10) and (8, 14)? (a) (12, 4) (b) (4, 2) (c) (4, 12) (d) (8, 24)
  26. 26.What is the distance between the points (3, 3) and (10, 27)? (a) 26 (b) 25 (c) 625 (d) 31
  27. 27.In which quadrant does the point (5, −8) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  28. 28.What is the distance between the points (3, 17) and (9, 9)? (a) 14 (b) 100 (c) 10 (d) 11
  29. 29.What is the midpoint of the line joining (8, 2) and (16, 8)? (a) (4, 3) (b) (12, 5) (c) (5, 12) (d) (24, 10)
  30. 30.How far is the point (7, 24) from the origin (0, 0)? (a) 26 (b) 25 (c) 625 (d) 31
  31. 31.What is the midpoint of the line joining (0, 8) and (12, 0)? (a) (7, 4) (b) (6, 4) (c) (12, 8) (d) (4, 6)
  32. 32.What is the distance between the points (9, 9) and (13, 12)? (a) 25 (b) 5 (c) 7 (d) 6
  33. 33.What is the midpoint of the line joining (7, 10) and (17, 20)? (a) (15, 12) (b) (12, 15) (c) (5, 5) (d) (24, 30)
  34. 34.What is the distance between the points (5, 9) and (13, 24)? (a) 289 (b) 18 (c) 23 (d) 17
  35. 35.What is the distance between the points (3, 11) and (27, 4)? (a) 26 (b) 625 (c) 25 (d) 31
  36. 36.What is the distance between the points (4, 0) and (12, 6)? (a) 11 (b) 14 (c) 10 (d) 100
  37. 37.What is the midpoint of the line joining (6, 6) and (18, 16)? (a) (6, 5) (b) (11, 12) (c) (24, 22) (d) (12, 11)
  38. 38.In which quadrant does the point (−8, 7) lie? (a) First quadrant (b) Third quadrant (c) Fourth quadrant (d) Second quadrant
  39. 39.What is the distance between the points (6, 32) and (13, 8)? (a) 26 (b) 31 (c) 625 (d) 25
  40. 40.What is the distance between the points (0, 3) and (12, 19)? (a) 21 (b) 400 (c) 20 (d) 28

Answer key

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

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