# Reflections review

Review the basics of reflections, and then perform some reflections.

### What is a reflection?

A reflection is a type of transformation that takes each point in a figure and reflects it over a line.
This reflection maps $\triangle{ABC}$ onto the blue triangle over the gold line of reflection.
The result is a new figure, called the image. The image is congruent to the original figure.

## Performing reflections

The line of reflection is usually given in the form $y = mx + b$.
Each point in the starting figure is the same perpendicular distance from the line of reflection as its corresponding point in the image.
Eksempel:
Reflect $\overline{PQ}$ over the line $y=x$.
First, we must find the line of reflection $y=x$. The slope is $1$ and the $y$ intercept is $0$.
When the points that make up $\overline{PQ}$ are reflected over the line $y=x$, they travel in a direction perpendicular to the line and appear the same distance from the line on the other side.
Note that in the case of reflection over the line $y=x$, every point $(a,b)$ is reflected onto an image point $(b,a)$.
Reflecting over the line $y=x$ maps $\overline{PQ}$ onto the blue line below.