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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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