Question

what was the scale factor used to create the dilation shown?

Explanation:

Step1: Find the length of a side of the original figure and the dilated figure

Let's consider the horizontal side. For the original figure (e.g., from \(B(-6,6)\) to \(C(6,6)\)), the length is \(6 - (-6)=12\) units. For the dilated figure (e.g., from \(B'(-2,2)\) to \(C'(2,2)\)), the length is \(2-(-2) = 4\) units.

Step2: Calculate the scale factor

The scale factor \(k\) is given by the formula \(k=\frac{\text{length of side in dilated figure}}{\text{length of side in original figure}}\). So \(k=\frac{4}{12}=\frac{1}{3}\)

Answer:

\(\frac{1}{3}\)