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Translation Demonstration: Polygon and Point Transformation

Translation Demonstration: Polygon and Point Transformation
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2017-03-08 21:25
PolygonVectorCoordinate GeometryTransformationGeometric Construction
This example demonstrates the translation transformation of geometric figures in a plane. Core concepts involve translation vectors, coordinate changes of corresponding points, and congruence properties. Construction utilizes GeoGebra commands like Polygon, Segment, Line, Circle, and Intersect to build the original figure and its image, highlighting the relationship between points A, B, C and their images A', B', C'. Suitable for middle and high school students learning geometric transformations and coordinate geometry.

GeoGebra Commands & Parameters

  1. Polygon(A, C, B) → poly1, c, a, b
  2. Segment(A', A) → f
  3. Line(C, f) → g
  4. Line(B, f) → h
  5. Circle(C, f) → d
  6. Circle(B, f) → e
  7. Intersect(d, g, 1) → C'
  8. Intersect(e, h, 1) → B'
  9. Segment(C, C') → i
  10. Segment(B', B) → j
  11. Polygon(A', C', B') → poly2, g_1, d_1, e_1

AI Drawing Prompt Reference

Draw a triangle ABC, then translate it to form a new triangle A'B'C'. First, draw triangle ABC. Then, draw point A', and draw a segment from A' to A as the translation vector. Use this vector to find points C' and B'. Finally, connect A', C', and B' to form triangle A'B'C'.
The prompt above was compiled from the original drawing commands and is for reference only.