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Triangle Centroid and Median Line Demo

Triangle Centroid and Median Line Demo
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2017-02-06 13:49
CircleVectorCoordinate GeometryOptimization
In collections Mapping Diagrams: From AB to C&DE, Resource
This example demonstrates the geometric properties of the centroid and median line of a triangle. Core math concepts include centroid, median line, vector operations, and coordinate geometry. It uses commands like Point, Vector, Textfield, Sequence, and Zip in GeoGebra to visualize the dynamic relationship between the centroid and median line via sliders. Suitable for high school mathematics teaching to understand geometric properties of plane figures and optimization problems.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Vector(A, B) → u
  3. Vector(B, C) → v
  4. Textfield(g) → inputBox1
  5. Textfield(f) → inputBoxf
  6. Vector(A, C) → w
  7. Sequence(0, n) → N
  8. Zip((0, y(A) - n / 2 + s), s, N) → x_n
  9. Zip(Vector[A, B], A, x_n, B, gx_n) → xu_n
  10. Zip(Vector[A, B], A, gx_n, B, fgx_n) → uy_n
  11. Zip(Vector[A, B], A, x_n, B, fgx_n) → xy_n