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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 ...
 
... and it doesn't matter what direction the mirror line goes, 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 different shapes about different mirror lines here:

Try it out to see what happens !

Note: If you cannot see this interactive graph, you will need to install "Flash Player"

 

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

 

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'

Mirror Image Prime

Some Tricks

Reflect About X Axis

X-Axis

If the mirror line is the x-axis, just change each (x,y) into (x,-y)

Y-Axis

If the mirror line is the y-axis, just change each (x,y) into (-x,y)

Reflect About Y Axis

Fold the Paper

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