Reflection

Reflections are everywhere ... in mirrors, glass, and here in a lake.
... what do you notice ?
Reflection in Lake Reflection Illustrated

Every point is the same distance from the central line !

... and ...

The reflection has the same size as the original image

The central line is called the Mirror Line ...

 

 

Can A Mirror Line Be Vertical?

Yes.
Here my dog "Flame" shows a
Vertical Mirror Line (with a bit of photo magic)

In fact Mirror Lines can be in any direction.
Imagine turning the photo at the top in different directions ...
... the reflected image is always the same size, it just faces the other way:

Left-Right Reflection   75 Degrees Reflection

 

A reflection is a flip over a line

You can try reflecting some shapes about
different mirror lines here:

View Larger

How Do I Do It Myself?

  Just approach it step-by-step. For each corner of the shape:
       
  1. Measure from the point to the mirror line (must hit the mirror line at a right angle) 2. Measure the same distance again on the other side and place a dot. 3. Then connect the new dots up!
  Step 1 Step 2 Final Reflect

Labels

Mirror Image Prime

It is common to label each corner with letters, and to use a little dash (called a Prime) to mark each corner of the reflected image.

Here the original is ABC and the reflected image is A'B'C'

Some Tricks

Reflect About X Axis

X-Axis

When the mirror line is the x-axis
we change each (x,y) into (x,−y)

 

Reflect About Y Axis

Y-Axis

When the mirror line is the y-axis
we change each (x,y) into (−x,y)

Fold the Paper

And when all else fails, just fold the sheet of paper along the mirror line and then hold it up to the light !