Chapter 6.8, Problem 9PPS

To determine

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

Answer to Problem 9PPS

New vertices will be $G^{\prime }\left(-2,2\right),H^{\prime }\left(4,2\right),J^{\prime }\left(6,-4\right),K^{\prime }\left(-4,-4\right)$

Explanation of Solution

Given information:$G\left(-1,1\right),H\left(2,1\right),J\left(3,-2\right),K\left(-2,-2\right);$ and scale factor is $k=2$

Calculation:

Here, the scale factor is $k=2$ .

Each coordinate will be multiplied by $2$ .

After dilation, points are transformed as shown below,

  $\left(x,y\right)\to \left(2x,2y\right).$

Apply this rule to transform the vertices.

  $\begin{array}{c}G\left(-1,1\right)\to G^{\prime }\left(-2,2\right)\\ H\left(2,1\right)\to H^{\prime }\left(4,2\right)\\ J\left(3,-2\right)\to J^{\prime }\left(6,-4\right)\\ K\left(-2,-2\right)\to K^{\prime }\left(-4,-4\right)\end{array}$

Hence, the new vertices is $G^{\prime }\left(-2,2\right),H^{\prime }\left(4,2\right),J^{\prime }\left(6,-4\right),K^{\prime }\left(-4,-4\right)$ .