Chapter 9.6, Problem 28PPS

(a)

To determine

To find: The scale factor of the dilation.

Answer to Problem 28PPS

The scale factor of the dilation is $2$ .

Explanation of Solution

The scale factor is calculated as,

  $\begin{array}{c}k=\frac{image}{pre-image}\\ =\frac{10}{5}\\ =2\end{array}$

Therefore, the scale factor is $2$ .

(b)

To determine

To find: The required grid size.

Answer to Problem 28PPS

The required grid size is $2.5\text{in}$ .

Explanation of Solution

The required grid size is calculated as,

  $\begin{array}{c}\text{Grid}\text{Size}=\frac{1}{4}\times 10\\ =\frac{5}{2}\\ =2.5\text{inch}\end{array}$

Therefore, the required grid size is $2.5\text{in}$ .

(c)

To determine

To find: The area of grid drawing.

Answer to Problem 28PPS

The area of grid drawing is $2240{\text{in}}^{\text{2}}$ .

Explanation of Solution

The scale factor is,

  $\begin{array}{c}\frac{1}{4}k=2\\ k=8\end{array}$

The area is,

  $\begin{array}{c}A=\left(5\times 8\right)\cdot \left(7\times 8\right)\\ =40\cdot 56\\ =2240{\text{in}}^2\end{array}$

Therefore, the area of the grid is $2240{\text{in}}^{\text{2}}$ .