Chapter 11.8, Problem 2GP

To determine

To find: Determine if the two figures are similar by using transformations.

Answer to Problem 2GP

A reflection and a Dilation with a scale factor of $k=2$ maps $\Delta DEF$ to $\Delta ABC$

Explanation of Solution

From Given figure

We get

From Triangle $ABC$

  $\begin{array}{l}AB=6\\ BC=6\\ CA=8.4\end{array}$

From $\Delta DEF$

  $\begin{array}{l}DE=3\\ EF=3\\ DF=4.2\end{array}$

If two polygons are similar then the ratio of the lengths of the two corresponding sides is the scale factor.

Ratio of lengths of each side are

  $\begin{array}{l}\frac{AB}{DE}=\frac{6}{3}\\ \Rightarrow \frac{AB}{DE}=2\end{array}$

  $\begin{array}{l}\frac{BC}{EF}=\frac{6}{3}\\ \Rightarrow \frac{BC}{EF}=2\end{array}$

  $\begin{array}{l}\frac{AC}{DF}=\frac{8.4}{4.2}\\ \Rightarrow \frac{AC}{DF}=2\end{array}$

As ratios are equal both triangles are similar using dilation with a scale factor of $k=2$

Here reflection also occurs.

So,

A reflection and a Dilation with a scale factor of $k=2$ maps $\Delta DEF$ to $\Delta ABC$