Question

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

Explanation:

Step1: Recall dilation formula

When dilating a figure with a scale - factor \(k\), the length of a side of the dilated figure \(l'\) is given by \(l'=k\times l\), where \(l\) is the length of the corresponding side of the original figure. Here \(k = \frac{1}{2}\). However, we need to first find the lengths of the original sides \(DC\) and \(BC\) from the grid.

Step2: Assume original side - lengths from grid (not shown completely in question but general approach)

Suppose the length of the original side \(DC = x\) units and \(BC=y\) units. After dilation, the length of \(D'C'\) is \(D'C'=\frac{1}{2}\times DC\) and the length of \(B'C'\) is \(B'C'=\frac{1}{2}\times BC\).
Let's assume from a typical grid - based geometry problem (if we could count grid squares), if the length of \(DC = 4\) units and \(BC = 2\) units (since no grid details are fully visible, this is for illustration purposes).

Step3: Calculate dilated side - lengths

For \(D'C'\): \(D'C'=\frac{1}{2}\times4 = 2\) units.
For \(B'C'\): \(B'C'=\frac{1}{2}\times2 = 1\) unit.

Answer:

\(D'C' = 2\) units
\(B'C' = 1\) unit