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Internal and External Division of a Line Segment

Internal and External Division of a Line Segment
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2018-08-01 23:59
Coordinate GeometryGeometric Construction
This example demonstrates the geometric construction and properties of internal and external division of a line segment. It involves core concepts like line segment division, distance calculation, special points, slope difference, and parametric curves. Key GeoGebra commands used include Segment, Point, and Distance to create segments and points, calculate distances (distanceAC), and label objects (text series). Points P, Q, R are used to show division points, while objects g, h, i illustrate parametric curves. Suitable for high school mathematics education to understand line segment division and parametric equations applications.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Point(f) → C
  3. Distance(A, C) → distanceAC
  4. Point({x(C), y(A)}) → P
  5. Point({x(B), y(A)}) → Q
  6. Point({x(B), y(C)}) → R
  7. Segment(A, P) → g
  8. Segment(P, Q) → h
  9. Segment(Q, R) → i
  10. Segment(R, B) → j
  11. Segment(A_1, B_1) → f_1
  12. Point(Line[A_1, B_1]) → C_1
  13. Distance(A_1, C_1) → distanceAC_1
  14. Segment(B_1, C_1) → k
  15. Point({x(B_1), y(A_1)}) → P_{1}
  16. Point({x(C_1), y(A_1)}) → Q_{1}
  17. Point({x(C_1), y(B_1)}) → R_{1}
  18. Segment(A_1, P_{1}) → l
  19. Segment(P_{1}, Q_{1}) → m
  20. Segment(Q_{1}, R_{1}) → n
  21. Segment(R_{1}, C_1) → p
  22. Segment(P_{1}, B_1) → q
  23. Segment(B_1, R_{1}) → r
  24. Segment(P, C) → s
  25. Segment(C, R) → t
  26. Segment(A_2, B_2) → f_2
  27. Point(Line[A_2, B_2]) → C_2
  28. Distance(A_2, C_2) → distanceAC_2
  29. Point({x(A_2), y(C_2)}) → P_2
  30. Point({x(B_2), y(C_2)}) → Q_2
  31. Point({x(B_2), y(A_2)}) → R_2
  32. Segment(A_2, P_2) → l_1
  33. Segment(P_2, Q_2) → m_1
  34. Segment(Q_2, R_2) → n_1
  35. Segment(B_2, R_2) → r_1
  36. Segment(C_2, P_2) → a
  37. Segment(A_2, R_2) → b
  38. Segment(A_2, C_2) → k_1