Another isometric transformation, a glide reflection, is a composition of a reflection and a translation.
- A
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reflection
can be described as a mirror image.
- A
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translation
can be described as a slide.
- Lines l and m are perpendicular.
- In the first example, pre-image Z is
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reflected
over line m.
- Image Z' is
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translated
along line m.
- In the second example, pre-image Z is
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translated
along line m.
- Image Z' is
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reflected
over line m.
Both examples show that pre-image Z is reflected and translated, creating a composition of two basic transformations.
- A glide reflection is the transformation created when a pre-image is reflected and translated over perpendicular lines.
A real world example:
- Each footprint is a reflection of the print made by the opposite foot translated one step forward.
- The composition of a reflection and a translation is a
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glide reflection
.