Chapter 6.8, Problem 12PPS

To determine

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

Answer to Problem 12PPS

New vertices will be $A^{\prime }\left(-\frac{3}{2},-\frac{5}{2}\right),B^{\prime }\left(0,1\right),C^{\prime }\left(\frac{3}{2},\frac{-1}{2}\right),D^{\prime }\left(0,-2\right)$

Explanation of Solution

Given information:

$A\left(-3,-5\right),B\left(0,2\right),C\left(3,-1\right),D\left(0,-4\right);$ and scale factor is $k=\frac{1}{2}$

Calculation:

Here, the scale factor is $k=\frac{1}{2}$ .

Each coordinate will be multiplied by $\frac{1}{2}$ .

After dilation, points are transformed as shown below,

  $\left(x,y\right)\to \left(\frac{1}{2}x,\frac{1}{2}y\right).$

Apply this rule to transform the vertices.

  $\begin{array}{c}A\left(-3,-5\right)\to A^{\prime }\left(-\frac{3}{2},-\frac{5}{2}\right)\\ B\left(0,2\right)\to B^{\prime }\left(0,1\right)\\ C\left(3,-1\right)\to C^{\prime }\left(\frac{3}{2},\frac{-1}{2}\right)\\ D\left(0,-4\right)\to D^{\prime }\left(0,-2\right)\end{array}$

Hence, the result is $A^{\prime }\left(-\frac{3}{2},-\frac{5}{2}\right),B^{\prime }\left(0,1\right),C^{\prime }\left(\frac{3}{2},\frac{-1}{2}\right),D^{\prime }\left(0,-2\right)$ .