Glide Reflection Demo by GeoGebra Institute of Hong Kong

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2014-08-03 10:22

In collections Symmetry, Transformation and Tessellation

This example demonstrates the effect of glide reflection on polygons, involving core math concepts like transformation, symmetry, vector, and coordinate geometry. It uses commands like Polygon, Vector, Line, Mirror, Translate, Sequence in GeoGebra for construction, suitable for high school students learning geometric transformations.

GeoGebra Commands & Parameters

Polygon(A, B, C, D) → poly1, a, b, c, d
Vector(E, F) → u
Line(E, F) → l
Mirror(A, l) → A'
Mirror(B, l) → B'
Mirror(C, l) → C'
Mirror(D, l) → D'
Polygon(A', B', C', D') → poly2, a', b', c', d'
Translate(A', u) → A''
Translate(B', u) → B''
Translate(C', u) → C''
Translate(D', u) → D''
Polygon(A'', B'', C'', D'') → poly3, a'', b'', c'', d''
Sequence(Polygon[Translate[A, Vector[((2 * n) * u)]], Translate[B, Vector[((2 * n) * u)]], Translate[C, Vector[((2 * n) * u)]], Translate[D, Vector[((2 * n) * u)]]], n, -5, 5) → list1
Sequence(Polygon[Translate[A'', Vector[((2 * n) * u)]], Translate[B'', Vector[((2 * n) * u)]], Translate[C'', Vector[((2 * n) * u)]], Translate[D'', Vector[((2 * n) * u)]]], n, -5, 5) → list2

AI Drawing Prompt Reference

Draw a quadrilateral, then create a vector and reflect the quadrilateral using this vector to get its mirror image. Translate the mirror image to get a translated quadrilateral. Finally, show the effect of translation by moving the original and translated quadrilaterals in multiple positions using the vector.

The prompt above was compiled from the original drawing commands and is for reference only.