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Coordinate Geometry Worksheet for Maths Olympiad

Maths Olympiad topic 28: Coordinates and distance · Set 61 · 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 (7, 27) and (14, 3)? (a) 26 (b) 25 (c) 625 (d) 31
  2. 2.What is the distance between the points (7, 5) and (13, 13)? (a) 11 (b) 100 (c) 14 (d) 10
  3. 3.In which quadrant does the point (−1, 3) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  4. 4.In which quadrant does the point (−5, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  5. 5.What is the distance between the points (0, 20) and (12, 4)? (a) 21 (b) 20 (c) 400 (d) 28
  6. 6.What is the midpoint of the line joining (2, 7) and (6, 3)? (a) (2, 2) (b) (8, 10) (c) (5, 4) (d) (4, 5)
  7. 7.How far is the point (5, 12) from the origin (0, 0)? (a) 14 (b) 169 (c) 17 (d) 13
  8. 8.What is the distance between the points (9, 16) and (18, 4)? (a) 225 (b) 16 (c) 21 (d) 15
  9. 9.What is the distance between the points (3, 1) and (11, 7)? (a) 11 (b) 10 (c) 100 (d) 14
  10. 10.In which quadrant does the point (9, −5) lie? (a) Second quadrant (b) Fourth quadrant (c) Third quadrant (d) First quadrant
  11. 11.In which quadrant does the point (−7, 3) lie? (a) Third quadrant (b) Fourth quadrant (c) Second quadrant (d) First quadrant
  12. 12.What is the distance between the points (3, 5) and (15, 0)? (a) 169 (b) 17 (c) 14 (d) 13
  13. 13.What is the distance between the points (3, 18) and (8, 6)? (a) 169 (b) 13 (c) 17 (d) 14
  14. 14.What is the midpoint of the line joining (2, 2) and (14, 10)? (a) (16, 12) (b) (8, 6) (c) (6, 4) (d) (6, 8)
  15. 15.How far is the point (8, 6) from the origin (0, 0)? (a) 100 (b) 11 (c) 14 (d) 10
  16. 16.How far is the point (12, 5) from the origin (0, 0)? (a) 13 (b) 17 (c) 169 (d) 14
  17. 17.What is the distance between the points (0, 3) and (8, 9)? (a) 10 (b) 100 (c) 11 (d) 14
  18. 18.In which quadrant does the point (−8, 7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  19. 19.What is the distance between the points (5, 9) and (8, 5)? (a) 7 (b) 5 (c) 6 (d) 25
  20. 20.How far is the point (6, 8) from the origin (0, 0)? (a) 100 (b) 14 (c) 11 (d) 10
  21. 21.In which quadrant does the point (8, 7) lie? (a) Second quadrant (b) First quadrant (c) Fourth quadrant (d) Third quadrant
  22. 22.What is the distance between the points (4, 0) and (11, 24)? (a) 26 (b) 25 (c) 625 (d) 31
  23. 23.What is the distance between the points (2, 3) and (11, 15)? (a) 16 (b) 21 (c) 225 (d) 15
  24. 24.What is the distance between the points (3, 4) and (18, 12)? (a) 18 (b) 23 (c) 17 (d) 289
  25. 25.How far is the point (15, 8) from the origin (0, 0)? (a) 289 (b) 17 (c) 18 (d) 23
  26. 26.What is the distance between the points (4, 5) and (10, 13)? (a) 10 (b) 11 (c) 14 (d) 100
  27. 27.In which quadrant does the point (4, 6) lie? (a) Fourth quadrant (b) Third quadrant (c) First quadrant (d) Second quadrant
  28. 28.In which quadrant does the point (3, 7) lie? (a) Third quadrant (b) First quadrant (c) Fourth quadrant (d) Second quadrant
  29. 29.What is the midpoint of the line joining (6, 1) and (14, 11)? (a) (4, 5) (b) (10, 6) (c) (6, 10) (d) (20, 12)
  30. 30.In which quadrant does the point (5, 5) lie? (a) First quadrant (b) Second quadrant (c) Fourth quadrant (d) Third quadrant
  31. 31.What is the midpoint of the line joining (1, 20) and (5, 10)? (a) (3, 15) (b) (6, 30) (c) (15, 3) (d) (2, 5)
  32. 32.What is the distance between the points (3, 6) and (27, 13)? (a) 25 (b) 31 (c) 26 (d) 625
  33. 33.What is the distance between the points (8, 11) and (12, 8)? (a) 25 (b) 5 (c) 7 (d) 6
  34. 34.In which quadrant does the point (−2, −4) lie? (a) Fourth quadrant (b) Second quadrant (c) First quadrant (d) Third quadrant
  35. 35.What is the midpoint of the line joining (8, 14) and (16, 10)? (a) (13, 12) (b) (4, 2) (c) (24, 24) (d) (12, 12)
  36. 36.In which quadrant does the point (7, −7) lie? (a) First quadrant (b) Fourth quadrant (c) Third quadrant (d) Second quadrant
  37. 37.In which quadrant does the point (8, −4) lie? (a) Third quadrant (b) First quadrant (c) Second quadrant (d) Fourth quadrant
  38. 38.What is the distance between the points (4, 14) and (12, 8)? (a) 11 (b) 14 (c) 10 (d) 100
  39. 39.How far is the point (24, 7) from the origin (0, 0)? (a) 625 (b) 26 (c) 25 (d) 31
  40. 40.What is the midpoint of the line joining (8, 11) and (12, 7)? (a) (2, 2) (b) (10, 9) (c) (9, 10) (d) (20, 18)

Answer key

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

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