3Sketch the translation of the triangle 5 units right and 1 unit up. In geometry, a transformation is a way to change the position of a figure. Students practice performing translations and reflections of triangles. How much are you translating and where is this line that you're reflecting over. 17 A TRANSLATION IS A CHANGE IN LOCATION. 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. 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. Translations and reflections are two of the few ways of how tessellations are created. So let's take a look at a common example of a glide reflection. You need to know every x and every y maps onto x plus some number and y plus some number. For example, f (x)x+5 is a isometry of the real line the whole line is shifted by 5 and distances between points remain unchanged. An isometry is a distance preserving map from some space it itself: a rigid motion. So you need to know two things to perform a glide reflection. The concepts of symmetry and isometry are central to the study of geometry. 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. You're not going to involve a rotation here. The Deformed Geometry and Moving Mesh interfaces are useful for modeling situations where a domain is deforming, as well as when it is moving in a completely. A special type of composition of transformations is a glide reflection and a glide reflection is the composition of a translation and a reflection.
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