Chapter 11.7, Problem 4GP

To determine

To find:Scale factor of the dilation.

Answer to Problem 4GP

Scale factor $=\frac{5}{8}$

Explanation of Solution

Given information:

Original dimensions of a poster $\left(x,y\right)=\left(8,14\right)$

Final dimensions of a poster $\left(x\text{'},y\text{'}\right)=\left(5,8\frac{3}{4}\right)$

Let $k$ be the Scale factor.

The dilation is $\left(x,y\right)\to \left(kx,ky\right)$ .

It means multiplying Original dimensions with Scale factor to get Final dimensions

Therefore,

  $\begin{array}{l}\left(x\text{'},y\text{'}\right)=\left(kx,ky\right)\\ \Rightarrow \left(5,8\frac{3}{4}\right)=\left(8k,14k\right)\end{array}$

On comparing

We get

  $\begin{array}{l}\Rightarrow 8k=5\\ \Rightarrow \frac{8k}{8}=\frac{5}{8}\\ \Rightarrow k=\frac{5}{8}\end{array}$

Therefore,

Scale factor $=\frac{5}{8}$