Graphing
Calculator
Math
Worksheets
Algebara
Solver
Chart
Maker
A+ A− B

Dilations in Math

How to perform dilations

What is a Dilation ?

Answer: A dilation is a type of transformation that changes the size of the image. The scale factor, sometimes called the scalar factor, measures how much larger or smaller the image is. Below is a picture of each type of dilation (one that gets larger and one that gest smaller)
Example 1
The picture below shows a dilation with a scale factor of 2. This means that the image, A', is twice as large as the pre-image A. Like other transformations, prime notation is used to distinguish the image fromthe pre-image. The image always has a prime after the letter such as A' .

Picture of a dilation in math

Example 2
Dilations can also reduce the size of shape. The picture below demonstrations a dilation of ½ Any time that the scale factor is a fraction, the image will get smaller.
Picture of a dilation in math

Formula for Dilations

It's always easier to understand a concept by looking at specific examples with pictures, so I suggest looking at the dilation examples below first...before you try to internalize the steps listed below and that explain the general formula for dilating a point with coordinates of (2,4) by a scale factor of 1/2.
1) multiply both coordiantes by scale factor (2 *½ ,4 *½)
2) Simplify (1,2)
3) Graph(if required)  

Demonstration of Dilation, Scale factor of 3


paus
animation of dilation by scale of 3

Practice Problems

Perform a Dilation of 3 on point A (2,1) which you can see in the graph below.
Answer



Perform a Dilation of 4 on point A (2,3) which you can see in the picture below.
Answer



Perform a Dilation of ½ on point A (2, 4) which you can see in the picture below.
Answer

Use the formula for dilations.
1) multiply both coordiantes by scale factor (2 *½ ,4 *½)
2) Simplify (1,2)
3) Graph(if required) see picture below


Perform a Dilation of 1/3 on point A (3,6) which you can see in the picture below.
Answer


What is the image of Triangle ABC graphed below after a dilation of ½?
Answer
Multiply each vertex by the scale factor of ½ ! And plot the new coordinates.
dilation of triangle

Compositions of transformations : dilations

Content on this page requires a newer version of Adobe Flash Player.

Get Adobe Flash player



Content on this page requires a newer version of Adobe Flash Player.

Get Adobe Flash player