Chapter 11.7, Problem 17IP

To determine

To find:Scale factor.

Answer to Problem 17IP

Scale factor $=k=\frac{2}{3}$

Dilation is a Reduction.

Explanation of Solution

Given information:

  $\begin{array}{l}A=\left(-3,3\right)\\ B=\left(3,3\right)\\ C=\left(3,6\right)\\ D=\left(0,6\right)\end{array}$

  $\begin{array}{l}A\text{'}=\left(-2,2\right)\\ B\text{'}=\left(2,2\right)\\ C\text{'}=\left(2,4\right)\\ D\text{'}=\left(0,4\right)\end{array}$

Let $k$ be the scale factor The dilation is $\left(x,y\right)\to \left(kx,ky\right)$ .

Multiply the coordinates of each vertex by $k$ .

  $\begin{array}{l}A\left(-3,3\right)\to A\text{'}\left(k\left(-3\right),k\left(3\right)\right)\\ \Rightarrow A\left(-3,3\right)\to A\text{'}\left(-3k,3k\right)\end{array}$

But given $A\text{'}=\left(-2,2\right)$

Therefore,

On comparing

We get

  $\begin{array}{l}-3k=-2\\ \Rightarrow \frac{-3k}{-3}=\frac{-2}{-3}\\ \Rightarrow k=\frac{2}{3}\end{array}$

As value of Scale factor lies between $0$ to $1$

It means Dilation is a Reduction.

Therefore,

Scale factor $=k=\frac{2}{3}$

Dilation is a Reduction.