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## Geometry (all content)

### Course: Geometry (all content)>Unit 10

Lesson 4: Reflections

# 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, A, B, C 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, equals, m, x, plus, b.
Each point in the starting figure is the same perpendicular distance from the line of reflection as its corresponding point in the image.
Example:
Reflect start overline, P, Q, end overline over the line y, equals, x.
First, we must find the line of reflection y, equals, x. The slope is 1 and the y intercept is 0.
When the points that make up start overline, P, Q, end overline are reflected over the line y, equals, 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, equals, x, every point left parenthesis, a, comma, b, right parenthesis is reflected onto an image point left parenthesis, b, comma, a, right parenthesis.
Reflecting over the line y, equals, x maps start overline, P, Q, end overline onto the blue line below.