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 ABC\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.
Want to learn more about different types of transformations? Check out this video.

Performing reflections

The line of reflection is usually given in the form y=mx+by = 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.
Reflect PQ\overline{PQ} over the line y=xy=x.
First, we must find the line of reflection y=xy=x. The slope is 11 and the yy intercept is 00.
When the points that make up PQ\overline{PQ} are reflected over the line y=xy=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=xy=x, every point (a,b)(a,b) is reflected onto an image point (b,a)(b,a).
Reflecting over the line y=xy=x maps PQ\overline{PQ} onto the blue line below.
Want to learn more about performing reflections? Check out this video.


Want to try more problems like this? Check out this exercise.