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Reflections in Math: Definition & Overview

Reflections in Math: Definition & Overview
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  • 0:00 What Are Transformations?
  • 1:00 Reflections
  • 1:34 How To Draw Reflections?
  • 3:31 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe
A reflection of an object is a 'flip' of that object across a line. This lesson will describe the basics of reflection, how to recognize one and how to create one.

What Are Transformations?

In geometry, a transformation is a copy of a geometric feature that holds certain properties. There are four main transformations:

  • Rotation: rotating an object about a fixed point, without changing its size or shape
  • Translation: moving an object in space without changing its size, shape or orientation
  • Dilation: expanding or contracting an object without changing its shape or orientation
  • Reflection: flipping an object about a line without changing its size or shape

When you are performing transformations, the initial object you start with is called the preimage. The final object, after the transformation, is called the image. Any transformation that does not change the size of the object is a rigid transformation. This includes rotations, translations, and reflections. A transformation that changes the size of the object, like a dilation, is called a non-rigid transformation.

Reflections

A reflection of an object is the 'flip' of that object over a line, called the line of reflection. In the following picture, the birds are reflected in the water.

Their image is flipped over the line created by the edge of the water. Lines of reflection do not have to be horizontal; they can also be vertical or sloped in any direction.

The following image shows a vertical line of reflection:

The next image shows a figure reflected twice. You can see that the red preimage is reflected to give the green image, and then, the green image is reflected again to give the second red image:

How To Draw Reflections?

Most reflections are drawn on the coordinate plane, which makes them easier to create. To draw a reflection, just draw each point of the preimage on the opposite side of the line of reflection, making sure to draw them the same distance away from the line as the preimage.

Here's an example:

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