Chapter 6.8, Problem 11PPS

To determine

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

Answer to Problem 11PPS

New vertices will be $R^{\prime }\left(-3,6\right),S^{\prime }\left(3,12\right),T^{\prime }\left(3,3\right)$

Explanation of Solution

Given information:

$R\left(-1,2\right),S\left(1,4\right),T\left(1,1\right);$ and scale factor is $k=3$

Calculation:

Here, the scale factor is $k=3$ .

Each coordinate will be multiplied by $3$ .

After dilation, points are transformed as shown below,

  $\left(x,y\right)\to \left(3x,3y\right).$

Apply this rule to transform the vertices.

  $\begin{array}{c}R\left(-1,2\right)\to R^{\prime }\left(-3,6\right)\\ S\left(1,4\right)\to S^{\prime }\left(3,12\right)\\ T\left(1,1\right)\to T^{\prime }\left(3,3\right)\end{array}$

Hence, the result is $R^{\prime }\left(-3,6\right),S^{\prime }\left(3,12\right),T^{\prime }\left(3,3\right)$ .