Question

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

Explanation:

Step1: Calculate length of side in original figure

Count the units of side \(BC\) in original figure. \(BC\) goes from \(x = - 6\) to \(x = 6\), so length \(BC=6 - (-6)=12\) units.

Step2: Calculate length of side in dilated figure

Count the units of side \(B'C'\) in dilated figure. \(B'C'\) goes from \(x=-2\) to \(x = 2\), so length \(B'C'=2-(-2) = 4\) units.

Step3: Find scale factor

Scale factor \(k=\frac{\text{length of dilated side}}{\text{length of original side}}\). So \(k=\frac{4}{12}=\frac{1}{3}\)

Answer:

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