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Segment Division

Segment Division
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2015-09-03 12:24
TrigonometryCoordinate GeometryCalculusGeometric Construction
This example demonstrates the geometric method to find a specific ratio point on a line segment, involving core math concepts like coordinate geometry, derivatives, cosine functions, and percentage calculations. It uses GeoGebra commands/objects such as Intersect, Midpoint, Circle, Line, and Segment for construction, suitable for high school and above students learning calculus, geometric constructions, and practical applications of ratios.

GeoGebra Commands & Parameters

  1. Intersect(a, b) → F
  2. Midpoint(A, F) → G
  3. Midpoint(C, B) → D
  4. Circle(D, Distance[D, C] + 1) → e
  5. Line(B, C) → f
  6. Intersect(e, f, 1) → E
  7. Intersect(e, f, 2) → H
  8. Segment(E, H) → g
  9. Line(A, g) → h
  10. Intersect(a, h) → I
  11. Midpoint(A, I) → J
  12. Circle(J, Distance[J, I] + 1) → k
  13. Intersect(k, h, 1) → K
  14. Intersect(k, h, 2) → L
  15. Segment(K, L) → i
  16. Segment(M, N) → j
  17. Midpoint(M, N) → O
  18. Segment(P, Q) → l
  19. Midpoint(P, Q) → R
  20. Midpoint(F, I) → S