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Coordinate Geometry Worksheet for Maths Olympiad

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

Answer key

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

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