Question

estimation without doing calculations, use side de and side de to estimate the scale factor for the dilation shown. then use two corresponding sides to find the scale factor.
side de looks about 3 times longer than side de. the scale factor for this dilation is
(simplify your answer.)

Explanation:

Step1: Understand the concept of scale factor

The scale factor \(k\) of a dilation is given by the ratio of the length of a side of the image (\(D'E'\)) to the length of the corresponding side of the pre - image (\(DE\)).

Step2: Use the given estimation

We are told that side \(D'E'\) looks about \(3\) times longer than side \(DE\). Mathematically, if we let \(l_{DE}\) be the length of \(DE\) and \(l_{D'E'}\) be the length of \(D'E'\), then the scale factor \(k=\frac{l_{D'E'}}{l_{DE}}\)

Answer:

\(3\)