When I think of reflections, the first thing I think of is a mirror. When you look in a mirror, you look at your reflection, which is an exact replica of yourself a certain distance away just in the opposite orientation. It's the same in a geometric reflection! A figure and its reflected image are equidistant from the line of reflection and they are orientated in flipped positions.
The key aspect of reflections is the equal distance of the original figure and the image figure to the line of reflection. Vanity mirrors also preserve this distance. A fun thing to think about is this image:
Why do passenger side mirrors make objects farther away? What must be different about the mirror?
Anyway, the students are going to investigate what happens when we reflect a figure over different lines such as the x-axis, y-axis, line y = x and line y = -x. Hopefully, they observe the respective patterns. To help, I have created some transparency squares:
I made these from transparent sheets like the ones my teachers used with overhead projectors in middle school and high school. I put decorative tape around the edges to avoid cutting fingers!!! So, using dry erase markers, students will draw the line of reflection and the figure; after, they can flip the whole transparency, match up the line of reflection, and see the reflected image. Students will then record the image points and observe how the coordinate values change.
We will investigate other techniques, like using a grid, for other vertical and horizontal lines in the plane. The challenge problem for the students will be to see if they can reflect a figure over a line in the form y = mx + b. We will discuss how the slopes relate between the line of reflection and segments created between original points and reflected points. If I had infinite time (if only), I would show students how to reflect over any line in 2D space using constructions.
To review the day's lesson, students will use the following online applets to check their understanding:
Anyone interested in the constructions can check out these YouTube videos. I found them very helpful!
Constructing a Line of Reflection:
Reflecting a Figure Over a Line in Space:
Here's to many more Geometry lessons in my future!
Miss Schuck
