Chapter 9.3, Problem 3CYU

To determine

To graph: The triangle DFG and its image after a rotation $180°$ about the origin.

Answer to Problem 3CYU

The triangle DFG and its image after a rotation is shown in Figure (1).

Explanation of Solution

The vertices of the triangle are $D\left(-2,6\right),F\left(2,8\right)\text{and}G\left(2,3\right)$ .

The coordinates of the new triangle after rotating by $180°$ is found by multiplying each coordinate of the vertices by $-1$ .

The new coordinates are $D^{\prime }\left(2,-6\right),F^{\prime }\left(-2,-8\right)\text{and}{G}^{\prime }\left(-2,-3\right)$ .

The graph of the triangles is shown below.

  

Figure (1)

Therefore, the triangle DFG and its image after a rotation is shown in Figure (1).