Chapter 9.6, Problem 18PPS

To determine

To find: Whether the dilation from W to $W^{\prime }$ is enlargement of a reduction and also find the factor of dilation and x.

Answer to Problem 18PPS

The dilation from W to $W^{\prime }$ is reduction and the factor of dilation is $0.33$ and the value of x is $4$ .

Explanation of Solution

The dilation is said to be enlargement is the scale factor is greater than $1$ and if smaller than $1$ it is a reduction.

Consider the given figure.

The scale factor is calculated as,

  $\begin{array}{c}k=\frac{F{W}^{\prime }}{FW}\\ =\frac{4}{12}\\ =0.33\end{array}$

The scale factor is smaller than $1$ so it’s a reduction.

The value of x is calculated as,

  $\begin{array}{c}x=12-8\\ =4\end{array}$

Therefore, the dilation from W to $W^{\prime }$ is reduction and the factor of dilation is $0.33$ and the value of x is $4$ .