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Triangle Reflection Across Axes Demo

Triangle Reflection Across Axes Demo
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2012-06-02 04:35
TrianglePolygonCoordinate GeometryTransformationGeometric Construction
In collections Reflections
① This example demonstrates the dynamic reflection of a triangle across the x‑axis, y‑axis, and the line y = x. ② Core mathematical concepts include plane reflection transformations, axial symmetry in coordinate geometry, and congruence of triangles. ③ Construction highlights: Polygon creates the original triangle; Mirror reflects points, segments, or the whole polygon about a given line (x‑axis, y‑axis, y = x); Point and Line define the reflection axes, producing successive reflected copies such as poly1', poly1'', etc. ④ Suitable for middle‑school geometry transformation lessons, high‑school analytic geometry review, and introductory GeoGebra animation projects.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a_1, b_1
  2. Mirror(A, a) → A'
  3. Mirror(B, a) → B'
  4. Mirror(C, a) → C'
  5. Polygon(A', B', C') → poly1', c', a', b'
  6. Mirror(A, yAxis) → A'_1
  7. Mirror(B, yAxis) → B'_1
  8. Mirror(C, yAxis) → C'_1
  9. Polygon(A'_1, B'_1, C'_1) → poly1'_1, c'_1, a'_1, b'_1
  10. Mirror(A, b) → A'_2
  11. Mirror(B, b) → B'_2
  12. Mirror(C, b) → C'_2
  13. Polygon(A'_2, B'_2, C'_2) → poly1'_2, c'_2, a'_2, b'_2
  14. Mirror(A, xAxis) → A'_3
  15. Mirror(B, xAxis) → B'_3
  16. Mirror(C, xAxis) → C'_3
  17. Polygon(A'_3, B'_3, C'_3) → poly1'_3, c'_3, a'_3, b'_3
  18. Polygon(D, E, F) → poly2, f_1, d_1, e_1
  19. Point(yAxis) → G
  20. Point(yAxis) → H
  21. Line(G, H) → j
  22. Point(xAxis) → I
  23. Point(xAxis) → J
  24. Line(I, J) → l