Question

pentagon abcde is the image of pentagon abcde under a dilation. what is the scale factor of the dilation?

Explanation:

Step1: Select corresponding sides

Let's consider side $AE$ and $A'E'$. Count the grid - units for each side. Side $AE$ has a length of 3 units (by counting the horizontal grid - units between $A$ and $E$), and side $A'E'$ has a length of 1 unit.

Step2: Calculate the scale factor

The scale factor $k$ of a dilation is given by the ratio of the length of the image side to the length of the pre - image side. So, $k=\frac{\text{length of }A'E'}{\text{length of }AE}$. Substituting the values, we get $k = \frac{1}{3}$.

Answer:

$\frac{1}{3}$