Question

gabriel is using a photo editing app to reduce the size of a photo. he dilates the photo by a scale factor of $\frac{1}{2}$ with the center of dilation at point $a$. what are the side lengths of the dilated photo? $dc=\text{ }$ units $bc = 2$ units

Explanation:

Step1: Recall dilation formula

The length of a dilated segment is the original - length times the scale - factor. Let the original length of a segment be \(l\) and the scale - factor be \(k\). Then the dilated length \(l'=k\times l\).

Step2: Assume original lengths

From the grid, assume the original length of \(DC\) is 2 units (by counting the grid - squares). The scale factor \(k = \frac{1}{2}\).

Step3: Calculate \(D'C'\)

Using the formula \(l'=k\times l\), substitute \(k=\frac{1}{2}\) and \(l = 2\). So \(D'C'=\frac{1}{2}\times2 = 1\) unit.

Answer:

\(D'C' = 1\) units