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 ...

reflection up-down

 

flame mirror center 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 top image in different directions:

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:

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 !