Chapter 12.6, Problem 4C

To determine

To graph : the $\Delta DEF$ with vertices $D\left(-6,-1\right),E\left(0,-2\right),F\left(-5,-4\right)$ ,and find coordinates of vertices of the image of $\Delta DEF$ after ${180}^{\circ }$ rotation and draw image.

Explanation of Solution

Given information : the verticesprovided in the question,

  $D\left(-6,-1\right),E\left(0,-2\right),F\left(-5,-4\right)$

Graph:

interpretation : in ${180}^{\circ }$ rotation multiply both x and y coordinates by -1.

Original image

  $\begin{array}{l}\left(x,y\right)\to \left(-x,-y\right)\\ D\left(-6,-1\right)\to D\text{'}\left(6,1\right)\\ E\left(0,-2\right)\to E\text{'}\left(0,2\right)\\ F\left(-5,-4\right)\to F\text{'}\left(5,4\right)\end{array}$