# Glide Reflection in Geometry: Definition & Example

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• 0:00 What Are Transformations?
• 2:11 What Are Glide Reflections?
• 3:22 Example
• 3:54 Lesson Summary
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Lesson Transcript
Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

In this lesson, we will look at transformations of geometric figures and concentrate on one type of transformation in particular: a glide reflection. Through a definition and examples, we will become comfortable with this type of transformation.

## What Are Transformations?

Before we get to talking about glide reflections, let's talk a bit about transformations. In mathematics, transformations are actions performed on a geometric figure that change the form of the figure, where a geometric figure is a set of points on a plane. There are four main types of transformations, and those are rotation, resizing, reflection, and translation.

When we perform a rotation on a geometric figure, we rotate, or turn, the figure around a fixed point. To picture this, consider drawing a square on a steering wheel, then rotating the steering wheel. We are rotating the square around the center of the steering wheel, which is a fixed point. This is a rotation.

Resizing a geometric figure can be thought of as the figure getting bigger or smaller, and can be done in a number of ways, including stretching, shrinking, dilating, or scaling. For example, consider a movie projector. The figures on the film are much smaller than they are when they appear on the screen. This is because the projector resizes the images.

The reflection transformation takes place when we reflect a geometric figure across a line called the axis of reflection. When we do this, we create a mirror image of the figure on the other side of the axis of reflection. You can probably guess the example that I am going to use for this one. That's right, a mirror! When we hold a picture of a geometric figure in front of a mirror, we can think of the mirror as the axis of reflection, and the figure gets reflected across to the other side of the mirror.

The last transformation is a translation. A translation of a geometric figure consists of simply sliding the figure along a straight line to a new location without changing anything else. The straight line that we want to slide the object across can be thought of as our translation rule. The length of the line tells us how far to slide the figure, and the orientation of the line tells us what direction to slide the figure. An example of a translation could be if you have a glass of water, and you slide it over a few inches. In doing this, you've translated the base of the glass. You haven't changed the shape of the base of the glass, you just moved it a few inches.

## What Are Glide Reflections?

Now that we have discussed transformations, we can talk about glide reflections. Glide reflections are a combination of two transformations: reflection and translation. This is somewhat apparent from the name. Glide can be thought of as sliding, which corresponds to a translation, and reflection simply corresponds to the reflection transformation. An easy way to remember how to perform a glide reflection is to remember to slide (translate) and flip (reflect). Slide and flip - easy as that!

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