Big Ideas Math Geometry, 2014
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Big Ideas Math Geometry, 2014 View details
2. Reflections
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Exercise 17 Page 187

A glide reflection is a transformation involving a translation followed by a reflection.

Practice makes perfect

To complete a glide reflection, we first perform the translation and then the reflection.

Translation

Let's begin by drawing â–ł RST.

The given rule of translation represents a vertical translation 1 unit down.

(x,y) → (x,y-1) To perform the translation, we have to subtract 1 from each y-coordinate.

Reflection

To reflect the quadrilateral in the given line, we will reflect its vertices. Recall that if a point (a,b) is reflected in the y-axis, then its image is (- a, b). With this, let's reflect each vertex of the triangle. &â–ł R'S'T' && â–ł R''S''T'' &R'(4,0) && R''(-4,0) &S'(7,2) && S''(-7,2) &T'(6,3) && T''(-6,3) Now that we know the reflected vertices, we can plot them and graph the image.

Final Glide Reflection

The final glide reflection is the combined translation and reflection.