Chapter 6.2, Problem 73SR

To determine

To graph: The pre-image and image of the quadrilateral.

Answer to Problem 73SR

The transformation of the graph represents the $180°$ rotation.

Explanation of Solution

Given:

The given figure is as follows.

  

Figure (1)

Calculation:

The vertex matrix is as follows.

  $\left[\begin{array}{cccc}2& 4& 2& -3\\ 3& -3& -5& -2\end{array}\right]$

Multiply the vertex matrix by $-1$ .

  $\left(-1\right)\left[\begin{array}{cccc}2& 4& 2& -3\\ 3& -3& -5& -2\end{array}\right]=\left[\begin{array}{cccc}-2& -4& -2& 3\\ -3& 3& 5& 2\end{array}\right]$

Therefore, the final vertex matrix is $\left[\begin{array}{cccc}-2& -4& -2& 3\\ -3& 3& 5& 2\end{array}\right]$ .

The graph of the pre-image and image is as follows.

  

Figure (2)

The transformation of the graph represents the $180°$ rotation.