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# Glide Reflections - Concept

###### 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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###### Brian McCall

B.S. in Chemical Engineering, University of Wisconsin

J.D. University of Wisconsin Law School (magna cum laude)

He doesn't beat around the bush. His straightforward teaching style is effective and his subtle midwestern accent is engaging. There's never a dull moment with him.

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