Chapter 9, Problem 33SGR

To determine

To find whether the figure is enlargement or reduction then find the scale factor of dilation and $x$ .

Answer to Problem 33SGR

Reduction, $x=8.25$ and $k=0.45$

Explanation of Solution

Given:

The given figure is-

  

Calculation:

Because figure W’ is smaller in size, so the dilation is the reduction.

By segment addition Postulate,

  $\begin{array}{l}FW=FW\text{'}+W\text{'}W\\ 15=6.75+x\\ x=8.25\end{array}$

Now, by definition of dilation-

  $\begin{array}{l}FW\text{'}=k(FW)\\ 6.75=k(15)\\ k=\frac{6.75}{15}\\ k=0.45\end{array}$