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Locus of the Centroid of an Equilateral Triangle

Locus of the Centroid of an Equilateral Triangle
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2019-04-18 03:35
TriangleGeometric ConstructionLocus
This example demonstrates the locus of the centroid of an equilateral triangle. Key mathematical concepts include centroid, rotation, and locus. Using GeoGebra commands such as Point, Rotate, and Locus, the dynamic movement of the centroid can be shown. Suitable for high school geometry courses.

GeoGebra Commands & Parameters

  1. Point(c) → P
  2. Rotate(c, 60°, P) → c'
  3. Remove(Ver, {P}) → V2
  4. Rotate(V2, -60°, P) → V3
  5. Sequence(Polygon[P, Element[V2, i], Element[V3, i]], i, 1, 3) → Trian
  6. Sequence(Centroid[Element[Trian, i]], i, 1, 3) → Bari
  7. Element(Bari, 1) → Bar
  8. Locus(Bar, P) → lugar1
  9. LocusEquation(Bar, P) → f