# Exploring Reflections with Desmos Activity Builder

Geometric transformations take up a good chunk of the first quarter of Geometry (at least the way that I had it sequenced). The tricky part of teaching transformations in Geometry is the delicate balance between the non-algebraic techniques and understandings and their algebraic counterparts.

For example, consider the two following statements.

Two images are reflections if they are congruent, equidistant from a single line of reflection and oriented perpendicularly from said line of reflection.

The reflection of A(x, y) is A'(-x, y) if the line of reflection is the y-axis and A'(x, y’) if the line of reflection is the x-axis.

As a geometry teacher, am I to prefer one over the other? In my experience, they both present challenges.Students are often a little more enthusiastic about the first (which is why I start there), but can often be more precise with the second. The second requires the figure to have vertices with coordinates and the line of reflection be an axis. The first requires the figure be drawn (and fairly accurately, at that.)

So, in my attempt to learn how to use Desmos Activity Builder, I wanted to produce something useful. So, I made a Desmos Activity to bridge the transition from a visual, non-algebraic understanding of reflections to an algebraic one.

Full disclosure: This activity presupposes that students are familiar with reflections in a visual sense. It isn’t intended to be an introduction to reflections for students who are brand new to the topic.

Feedback, questions… all welcome.

## 5 thoughts on “Exploring Reflections with Desmos Activity Builder”

1. See my latest post about an improved GEOSTRUCT, the application I have been working on (and off) for a long time. Especially Rigid Motions. Or just click this:
mathcomesalive.com/geostruct/geostructforbrowser1.html

• Problem here, looks like you’ll have to paste it.

• Awesome, thanks! I look forward to checking this out!

2. I like the activity. I would just mention that possibility of having Desmos actually carry out the reflections using a draggable point: https://www.desmos.com/calculator/uvtgj8lmuw
You might consider ending with a challenge problem for advanced students to find a rule that will give them the image of a point (a,b) if they reflect across the line x=2.

• I appreciate the suggestions. I suspected there was a way to automate reflections. Thanks for giving me an example of how to make it happen!