Dilation Rules
Explained w/ 13 Step-by-Step Examples!

In this geometry lesson, you’re going to learn all about Dilation Rules!

Jenn, Founder Calcworkshop^®, 15+ Years Experience (Licensed & Certified Teacher)

More specifically, you’re going to explore how to apply scale factors to calculate enlargements and reductions.

Finally, you’re going to use techniques to find missing variables within the given problems.

So let’s get started!

Did you know that dilations are all around us?

Whenever we want to zoom and enlarge a photo so you can see details, we are using a dilation transformation.

At eye exams, the pupil dilates (widens), allowing in more light and giving your doctor a better view of the back of your eye.

When you build model airplanes, cars, or buildings that are true in scale and measurement, you are performing a dilation.

And even your shadow is a dilation as well.

What Is A Dilation

A dilation is a transformation that enlarges or reduces a figure in size. This means that the preimage and image are similar and are either reduced or enlarged using a scale factor.

As seen in the graphics below. A reduction (think shrinking) is a dilation that creates a smaller image, and an enlargement (think stretch) is a dilation that creates a larger image.

Dilation Reduction

Dilation – Enlargement

How To Find The Scale Factor Of A Dilation

To find the scale factor for a dilation, we find the center point of dilation and measure the distance from this center point to a point on the preimage and also the distance from the center point to a point on the image. The ratio of these distances gives us the scale factor, as Math Bits Notebook accurately states.

Using dilation scale factors, we can shrink or expand a figure to the size we desire, knowing that each angle is congruent, each segment is proportional, the slope of each segment is maintained, and the perimeter of the preimage and image have the same scale factor.

How to Find the Scale Factor

Next, you’ll learn how to perform the following operations:

1. Determine the scale factor for the transformation.
2. Identify the type of dilation.
3. Draw a dilation using a scale factor.
4. Find the ratio of perimeters for two dilated figures.

Video – Lesson & Examples

44 min

• Introduction to Dilations
• 00:00:20 – What are Dilations? How to find the Scale Factor?
• Exclusive Content for Member’s Only

• 00:07:40 – Given the scale factor, determine if the dilation is a reduction or enlargement (Examples #1-4)
• 00:09:48 – Identify the dilation and determine its scale factor (Examples #5-7)
• 00:13:53 – Graph the dilation with the origin as the center point (Examples #8-9)
• 00:20:02 – Find the scale factor given select vertices from the preimage and image (Examples #10-11)
• 00:28:27 – Given a dilation solve for the indicated variables and find the ratio of perimeters (Examples #12-13)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions