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Verify the Centroid of Triangle ABC

Verify the Centroid of Triangle ABC
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2014-11-04 00:16
TriangleCoordinate GeometryGeometric Construction
This example demonstrates how to verify the centroid of triangle ABC with vertices A(-2, 4), B(5, 4), and C(3, -2) using GeoGebra commands such as Polygon, Line, Segment, Midpoint, Intersect, etc. Key mathematical concepts include the definition and calculation of the centroid of a triangle. Suitable for students at the junior high school level and above in coordinate geometry.

GeoGebra Commands & Parameters

  1. Polygon((instructionEdge, y(Corner[1])), Corner[2], Corner[3], (instructionEdge, y(Corner[4]))) → instruction, instructionBottom, instructionRight, instructionTop, instructionLeft
  2. Line((instructionEdge + ((4 * indent) * screenwidth), 0), yAxis) → align3
  3. Line((instructionEdge + ((3 * indent) * screenwidth), 0), yAxis) → align2
  4. Line((instructionEdge + ((2 * indent) * screenwidth), 0), yAxis) → align1
  5. Segment(A, B) → a
  6. Segment(B, C) → b
  7. Segment(C, A) → c
  8. Midpoint(a) → T
  9. Midpoint(c) → V
  10. Midpoint(b) → U
  11. Line(T, C) → e
  12. Line(U, A) → f
  13. Intersect(f, e) → X
  14. Line(V, B) → d
  15. GCD(AUdistance2, AXdistance2) → Agcd
  16. GCD(BXdistance2, BVdistance2) → Bgcd