Chapter 6.8, Problem 7PPS

To determine

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

Answer to Problem 7PPS

New vertices will be $X^{\prime }\left(3,3\right),Y^{\prime }\left(\frac{9}{2},6\right),Z^{\prime }\left(6,0\right)$

Explanation of Solution

Given information:

  $k=\frac{3}{4}$

Given graph

Calculation:

Here, the scale factor is $k=\frac{3}{4}$ .

Each coordinate will be multiplied by $\frac{3}{4}$ .

After dilation, points are transformed as shown below,

  $\left(x,y\right)\to \left(\frac{3}{4}x,\frac{3}{4}y\right).$

Apply this rule to transform the vertices.

  $\begin{array}{c}X\left(4,4\right)\to X^{\prime }\left(3,3\right)\\ Y\left(6,8\right)\to Y^{\prime }\left(\frac{9}{2},6\right)\\ Z\left(8,0\right)\to Z^{\prime }\left(6,0\right)\end{array}$

Graphs are as shown below.