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)
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'.
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.
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)|
|3) Graph(if required)|
Demonstration of Dilation, Scale factor of 3
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)
Multiply each vertex by the scale factor of ½ ! And plot the new coordinates.