Chapter 11.7, Problem 5GP

To determine

To find: Scale factor of the dilation.

Answer to Problem 5GP

Scale factor $=\frac{5}{2}$

Explanation of Solution

Given information:

Original dimensions of a painting $\left(x,y\right)=\left(14,22\right)$

Final dimensions of a painting $\left(x\text{'},y\text{'}\right)=\left(35,55\right)$

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,

  $\begin{array}{l}\left(x\text{'},y\text{'}\right)=\left(kx,ky\right)\\ \Rightarrow \left(35,55\right)=\left(14k,22k\right)\end{array}$

On comparing

We get

  $\begin{array}{l}\Rightarrow 14k=35\\ \Rightarrow \frac{14k}{14}=\frac{35}{14}\\ \Rightarrow k=\frac{35}{14}\\ \Rightarrow k=\frac{5}{2}\end{array}$

Therefore,

Scale factor $=\frac{5}{2}$