Two Reflections Equal One Translation

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2014-07-03 04:42

This example demonstrates that two reflections can result in one translation. Key mathematical concepts include reflection, translation, and geometric transformations. It uses commands like Polygon, Mirror, Vector, and Translate in GeoGebra. Suitable for middle school and above students to learn geometric transformations.

GeoGebra Commands & Parameters

Polygon(A, B, C, D) → poly1, a, b, c, d
Mirror(A, e) → A'
Mirror(B, e) → B'
Mirror(C, e) → C'
Mirror(D, e) → D'
Polygon(A', B', C', D') → poly1', a', b', c', d'
Mirror(A', f) → A''
Mirror(B', f) → B''
Mirror(C', f) → C''
Mirror(D', f) → D''
Polygon(A'', B'', C'', D'') → poly1'', a'', b'', c'', d''
Vector(D, D'') → u
Translate(A, u) → A'_1