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# Translations - 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 **geometry translation** is an isometric transformation, meaning that the original figure and the image are congruent. Translating a figure can be thought of as "sliding" the original. If the image moved left and down, the rule will be (x - __, y - __) where the blanks are the distances moved along each axis; for translations left and up: (x - __, y + __), for right and down (x + __, y - __), for right and up (x + __, y + __).

There are 4 types of transformations, three of which are isometries. One of these is a translation, so a translation is an isometry that slides or moves over the points on a figure in the same direction so let's say I gave names to my 3 vertices in this triangle let's call this a, b and c so notice if go in a clockwise direction after a follows b, after b follows c, after c follows a. When I translate this that orientation is going to stay the same. We're still going to have a then b, b then c and c then a. But how do we describe a translation of the mathematicians? Well to do that, we're going to write an expression kind of like this which says the original coordinates whatever they are x and y are being mapped on to a new image so this tells me to take every x coordinate of this triangle and add 1 to it. Tells me to take every y coordinate of this triangle and subtract 2 so you're going to use this rule to find which way you're going to translate.

When you're adding to an x you'll be shifting your figure to right, when you're subtracting from x you're going toshift your figure to the left. When y is being added to you're going to shift your figure up and when y is being subtracted it'll shift your figure down, so keep that in mind when your problems that are asking you to translate an image.

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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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