In the mirror

         All those old 9th grade frustrations are resurfacing again. I did the math today, and it's been 23 years since I've had to think about any of these geometry concepts. I was able to do them okay then and now, but I have never felt confidence in explaining them, or even confidence that I fully understand them. Anyways, back to the mirror. Reflections are a funny thing. When I look in the mirror, I think I see myself, and don't even consciously consider that what I am actually seeing is a reflection. I had to alter my thoughts for this lesson.
          Within the realm of math and geometry, a reflection is thought of as a flipping or folding of a shape over the line of reflection. That means that when I am asked to perform a reflection, the most important things for me to consider are the line of reflection (or mirror line), and where the shape's vertices fall on the grid in respect to the line of reflection. This means that if I have a shape with vertices at (-5,2), (-3,-3) and (-1,2) and I want to do a reflection of this triangle across the y-axis, I'm going to need to look closely at those points. A basic rule for reflecting over the y-axis will be that each point's mirror will be as follows: (x,y) mirrored to (-x,y). That means for the triangle above, my reflection vertices would be (5,2), (3,-3), and (1,2). If I was reflecting across the x-axis, the rule would be (x,y) mirrored to (x,-y).  I found this awesome chart to help with a few of the other common mirror lines and the rules for finding new coordinates here.

Outside of these common lines of reflection, a person would have to see where the image sits in relation to the mirror line in order to find the mirror image across a different line of reflection. If all else fails, students could try folding their paper along the line of reflection to see where placement for the mirror image should be. Good luck! If you need me I'll be staring at my reflection in the mirror, admiring all my new grey hairs thanks to geometry!