Act 1

Take a Look at the image of the Mirror below and read the info that follows!

Mirrors are known for showing us our reflection. You probably wouldn't know what you looked like without one. And it would make it incredibly hard to get ready in the morning!

Have you ever noticed though, that the "virtual" you inside the mirror looks like it is exactly the same distance from the mirror as you are? Go test it out, find a mirror and step closer and further away from it. Is the virtual you doing the same and more importantly, does the virtual you look to be the same distance from the mirror as you are!? If you have a mirror that isn't bent or warped in any way this should be the case!

So why do we care? Well, in math we are concerned with reflections as well. Only we aren't talking about reflections in a mirror, we are talking about reflections across an axis.

Take a look at the mirror below

Let's pretend the center of the mirror is our Y-axis. Now draw an imaginary line from the object to the virtual image. Which axis does it cross? ….That’s right, it crossed the Y axis. Do you see how the object and the virtual object are exactly the same distance from the Y-axis? For this reason, this is called a reflection across the Y-axis.

How about this next image?

This time pretend the center of the mirror is our X-axis. Now draw an imaginary line from the object to the virtual image. Which axis does it cross? ….That’s right, it crossed the X-axis. Do you see how the object and the virtual object are exactly the same distance from the x-axis? For this reason, this is called a reflection across the x-axis.

Now you give it a try.

For each of the pairs of coordinates, do the following:

1. Graph both coordinate pairs
2. State which coordinate, the x or the y changed signs
3. Draw a dotted line from the first point to the second. State which axis it crossed. (i.e. Pair E is a reflection across the x-axis)

After completing the questions for A,B,C &D answer the following

4. Is there a way to tell what axis two points are reflected across without graphing those points? If so, please state how you know.