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Glide Reflections - Concept

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

A glide reflection is a composition of transformations.In a glide reflection, a translation is first performed on the figure, then it is reflected over a line. Therefore, the only required information is the translation rule and a line to reflect over. A common example of glide reflections is footsteps in the sand.

A special type of composition of transformations is a glide reflection and a glide reflection is the composition of a translation and a reflection. Only those two. You're not going to involve a rotation here.
The key thing to a glide reflection is that this reflection has to be over a line that's parallel to the direction that you're translating. So you need to know two things to perform a glide reflection.
The first one is a translation rule. You need to know every x and every y maps onto x plus some number and y plus some number. You also need a line to reflect over. So let's take a look at a common example of a glide reflection.
If I started with a foot although it's not very well drawn, if I translated it, a little bit in this direction and then if I reflected it over this line and I redrew it down below, 1, 2, 3, 4 and a big toe, then you can see that as I keep going on with this translation and then a reflection. So now I'm going to redraw this again. I'm going to have big toe 1, 2, 3, 4 and again I never said this is an art class, it's pretty clear that foot steps represent a glide transformation, because we are translating, reflecting. Translating, reflecting.
So you only need to know 2 things. How much are you translating and where is this line that you're reflecting over.

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