#### What is a Dilation?

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'.

##### Example 2

Dilations can also reduce the size of shape. The picture below demonstrations a dilation of $$ \frac{1}{2}$$ Any time that the scale factor is a fraction, the image will get smaller.

**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 $$\red { \frac 1 2 }$$.

1) multiply both coordiantes by scale factor | ($$2 \cdot \red { \frac 1 2 } ,4 \cdot \red { \frac 1 2 }$$) |

2) Simplify | (1,2) |

3) Graph(if required) |

### Demonstration of Dilation, Scale factor of 3

**Practice** Problems

Multiply the coordinates of the original point (2,1), called the image, by 3.

Image's coordinates = (2 *3, 1*3 ) to get the coordinates of the image (6, 3)

Multiply the coordinates of the original point (2,3), called the image , by 4.

Image's coordinates = (2 *4, 3*4 ) to get the coordinates of the image (8, 12)

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 |

Use the formula for dilations.

1) multiply both coordiantes by scale factor | (3 *1/3 ,6 *1/3) |

2) Simplify | (1,2) |

3) Graph(if required) | see picture below |

Multiply each vertex by the scale factor of ½ ! And plot the new coordinates.