Chapter 9.6, Problem 33PPS

(a)

To determine

To find: The scale factor of the dilation.

Answer to Problem 33PPS

The scale factor is $1.33$

Explanation of Solution

The scale factor is calculated as,

  $\begin{array}{c}k=\frac{image}{pre-image}\\ =\frac{2}{1.5}\\ =1.33\end{array}$

Therefore, the scale factor is $1.33$ .

(b)

To determine

To find: The cross section area before and after dilation.

Answer to Problem 33PPS

The area before dilation is $1.77{\text{mm}}^2$ and after dilation is $3.14{\text{mm}}^2$ .

Explanation of Solution

The area before dilation is,

  $\begin{array}{c}{A}_{\text{before}}=\pi {\left(0.75\right)}^2\\ =1.77{\text{mm}}^2\end{array}$

The area after dilation is,

  $\begin{array}{c}{A}_{\text{after}}=\pi {\left(\frac{3}{4}\times \frac{4}{3}\right)}^2\\ =3.14{\text{m}}^2\end{array}$

Therefore, the area before dilation is $1.77{\text{mm}}^2$ and after dilation is $3.14{\text{mm}}^2$ .