Transformations

Objectives:

Define reflection, rotation, translation, and dilation
Identify the type of transformation performed on a given figure
Determine the new coordinates of a figure that has been reflected, rotated, translated, or dilated
Determine the scale factor of a dilation

What are transformations?
A transformation takes a figure and manipulates it by moving it in the coordinate plane. There are four types of transformations: reflections, rotations, translations, and dilations.

Three of the transformations are called "rigid transformations". This means that the figure will preserve its size when it is transformed. Unlike rigid transformations, dilations affect the size of the figure.

A.) The Four Types of Transformations

B.) Identifying the Transformation:

We can identify the type of transformations performed on a figure by comparing the "pre-image" with the "image". Let's look at some examples:

Practice Problems B

For each graph below, identify and describe the type of transformation:

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C.) Performing a Transformation:

Now that you have learned how to identify a transformation, you will be performing a transformation on a given figure. You will be given two pieces of information: (1) A figure and (2) The type of transformation. You will use this information to perform a transformation in order to find the resulting image.

Practice Problems C

:For each graph below, determine the resulting image by performing the given transformation:

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D.) The Transformations Rules

You just learned that we can determine the type of transformations on a pre-image by comparing the pre-image and image. There is an alternative way that we can also determine the type of transformation. This approach includes a given set of "transformation rules". We can also use these rules to determine the coordinates of the image given the pre-image and type of transformation performed. Let's look at the rules and some examples!

Practice Problems D

Given the pre-images below, determine the coordinates of the images after the transformations are performed: