Question

1. what is the scale factor for the dilation?

Explanation:

Step1: Select corresponding sides

Let's take side $AE$ and $A'E'$. Assume each grid - square side length is 1 unit. $AE = 4$ units and $A'E'=2$ units.

Step2: Calculate scale factor

The scale factor $k$ of a dilation is given by the ratio of the length of a side in the image to the length of the corresponding side in the pre - image. So $k=\frac{\text{length of side in image}}{\text{length of corresponding side in pre - image}}=\frac{A'E'}{AE}$.
Substitute the values: $k = \frac{2}{4}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$