Reflection

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

Mountain reflection marked with yellow lines showing equal distances from points to the water line

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:

An asymmetrical shape reflected across a horizontal mirror line

Can A Mirror Line Be Vertical?

Dog face mirrored vertically down the center to show symmetry

Yes. Here my dog "Flame" shows a vertical mirror line (with a bit of photo editing).

In fact mirror lines can be in any direction.
Imagine turning the top image in different directions:

An asymmetrical shape reflected across a vertical mirror line

An asymmetrical shape reflected across a slanted mirror line

A reflection is a flip over a line

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

images/reflect.js

"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)
Measuring the perpendicular distance from a shape's vertex to the mirror line

Measuring the perpendicular distance from a shape's vertex to the mirror line

2. Measure the same distance again on the other side and place a dot.
Marking the exact same distance on the opposite side of the mirror line

3. Then connect the new dots up!
Connecting the reflected vertices to form the complete mirrored shape

When measuring the distance go straight to the mirror line at a 90° right angle.

Labels

Triangle ABC reflected across a line to form triangle A'B'C'

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

Imagine a point at (2, 5). If you reflect it across the x-axis (the horizontal line), which coordinate will change? The 2 or the 5?

Triangle reflected across the x-axis, changing sign of y-coordinates

X-Axis

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

Triangle reflected across the y-axis, changing sign of x-coordinates

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 !

6716, 6717, 3346, 3344, 3345, 3347, 5152, 5153, 841, 842