Math CSET 2 How to Transform Polygons with Matricies

At some point in the test the ability to do matrix transformations of a 2-dimensional polygon will come in handy.  Here are the most useful transformations and what they do.

First of all:

You need to have your polygon in matrix form in order to apply a matrix transformation.  This just means compile a list of the verticies with x on top and y on bottom with square brackets on each end like so:

polygon to matrix

In order to now transform the polygon with any matrix transformation we will use matrix multiplication.  Multiply the polygon matrix by the transformation matrix.  Math in words makes almost no sense so here are some examples of the most common transformations.

Dilation:

This takes every vertex of the figure and either shrinks it or enlarges it just like this object which is the most fun thing on the planet to play with.

expanding ball

Using matricies dilate this polygon by 2:

Take your polygon matrix and multiply every entry by the dilation factor to get your new matrix.

polygon dialation with matrix

Translation or slide:

usher slide

Slide the polygon around the coordinate plane.  First start off with you polygon matrix, know the translation you want to perform.  Then add the x translation to all x values and the y translation to all y values.

Translate the polygon up 3 and left 2:

In the polygon matrix up 3 is add 3 to every y value and left 2 is subtract 2 from every x value.  Your new matrix will be your translated polygon.

translate polygon with matrix

Reflections:

mirror mirror on the wall

Each type of reflection will have its own matrix to multiply the polygon by.  Do matrix multiplication with the reflection matrix to get your new reflected polygon matrix.

Relfection matricies

Rotations:

In a similar manner to rotate your polygon with a matrix multiply your polygon matrix by the rotation matrix of your choice. The first is a rotation 90 degrees counter clockwise.

rotation matricies

As always practice makes perfect, especially when it comes to remembering all the different matricies.  Do about five problems with each transformation and that should commit them to memory.  Otherwise try etching them into a stone tablet.

Share with everyone you know.  We need more math teachers!

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