Chapter 6.8, Problem 8PPS

To determine

To find: The vertices of given figure after a dilation with the given scale factor $k$ .

Answer to Problem 8PPS

New vertices will be $K^{\prime }\left(\frac{5}{3},0\right),L^{\prime }\left(\frac{8}{3},1\right),M^{\prime }\left(1,\frac{8}{3}\right),N^{\prime }\left(0,\frac{5}{3}\right)$

Explanation of Solution

Given information:

  $k=\frac{1}{3}$

Given graph

Calculation:

Here, the scale factor is $k=\frac{1}{3}$ .

Each coordinate will be multiplied by $\frac{1}{3}$ .

After dilation, points are transformed as shown below,

  $\left(x,y\right)\to \left(\frac{1}{3}x,\frac{1}{3}y\right).$

Apply this rule to transform the vertices.

  $\begin{array}{c}K\left(5,0\right)\to K^{\prime }\left(\frac{5}{3},0\right)\\ L\left(8,3\right)\to L^{\prime }\left(\frac{8}{3},1\right)\\ M\left(3,8\right)\to M^{\prime }\left(1,\frac{8}{3}\right)\\ N\left(0,5\right)\to N^{\prime }\left(0,\frac{5}{3}\right)\end{array}$

Graphs are as shown below.