Transformations with Matrices

28 Sep

We finished up our unit on Rigid Motions by taking a brief look at transformations using matrices. At the beginning of class, we made sure each student could transform a given point in the coordinate plane and generalize the transformation.

Screen Shot 2013-09-28 at 1.43.58 PM

Screen Shot 2013-09-28 at 1.43.49 PM

Our students do not have any experience multiplying matrices. I didn’t want to get into a huge lesson on multiplying matrices, but I also wanted my students to realize that they had the background they needed to make sense of transforming triangles using matrices.

We used TI-Nspire technology to look for regularity in repeated reasoning. We started by multiplying the matrix that represented the vertices of our triangle (1,4), (4,–3), and (–2,5) by the matrix shown to observe how matrix multiplication works.

Screen Shot 2013-09-28 at 2.41.17 PM

By what matrix should we multiply if we want the output to be the vertices of the triangle after it has been reflected about the x-axis?

It took NR only two tries before she got the correct transformation matrix. It took others more than two tries. But once students had the matrix for a reflection about the x-axis, it didn’t take long to get the matrix for a reflection about the y-axis.

09-28-2013 Image016


And then reflections about the lines y=x and y=-x.


09-28-2013 Image017


And then rotations 90 degrees and -90 degrees about the origin.

09-28-2013 Image018

I honestly do not care that students remember the matrix that produces a certain transformation. I am not even sure that I should have spent any class time on this topic (although I have seen questions on some state assessments about this topic). What I care about is that students know that they can make sense of problems and persevere in solving them. I care that they know that they can figure out the matrix that produces a certain transformation instead of me giving them a list to memorize.

Screen Shot 2013-09-28 at 1.43.36 PM

And so the journey to create students who can figure out mathematics instead of being told mathematics continues …


Posted by on September 28, 2013 in Coordinate Geometry, Geometry, Rigid Motions


Tags: , , , ,

2 responses to “Transformations with Matrices

  1. Travis

    September 28, 2013 at 8:09 pm

    I don’t know if this would help or hurt! But those transformation matrices can be named. Since they are a ‘bunch of +1 and -1’s all moved about’, maybe an extension for some students would be name them all, and then see if they work. The decimal point can be used once I think. rot90ccw or reflect.x They can be easily accessed under var. All of which I think you know, but just wanted to add another column to your chart. I am not entirely convinced of the pedagogy, but it gives me something to think about.


Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: