# The dashed triangle is the image of the solid triangle. The center of dilation is (−4,−4). What is the scale factor used to create the dilation?

Sep 23, 2016

$S F = - 3$

#### Explanation:

Looking at the figure and its image, three things are immediately obvious.....
The image is bigger
The image is inverted.
The figure and the image have a common point.

The common point is the centre of dilation.$\left(- 4 , - 4\right)$
The fact that it lies BETWEEN the image and the figure means that the SF is a negative number.
This accounts for the fact that the image is inverted.

To find the Scale Factor divide $\left(\text{a side in the image")/("the same side in the figure}\right\}$

Looking at the horizontal lines we see..

$\left(\text{a side in the image")/("the same side in the figure}\right\} = - \frac{6}{2} = - 3$