Chapter 6.8, Problem 10PPS

To determine

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

Answer to Problem 10PPS

New vertices will be $W^{\prime }\left(0,0\right),X^{\prime }\left(2,-2\right),Y^{\prime }\left(2,4\right)$

Explanation of Solution

Given information:

$W\left(0,0\right),X\left(5,-5\right),Y\left(5,10\right)$ and scale factor is $k=\frac{2}{5}$

Calculation:

Here, the scale factor is $k=\frac{2}{5}$ .

Each coordinate will be multiplied by $\frac{2}{5}$ .

After dilation, points are transformed as shown below,

  $\left(x,y\right)\to \left(\frac{2}{5}x,\frac{2}{5}y\right).$

Apply this rule to transform the vertices.

  $\begin{array}{c}W\left(0,0\right)\to W^{\prime }\left(0,0\right)\\ X\left(5,-5\right)\to X^{\prime }\left(2,-2\right)\\ Y\left(5,10\right)\to Y^{\prime }\left(2,4\right)\end{array}$

Hence, the result is $W^{\prime }\left(0,0\right),X^{\prime }\left(2,-2\right),Y^{\prime }\left(2,4\right)$ .