Chapter 4.4, Problem 33PPS

To determine

To find: The coordinates of the vertices after the reflection in the given axis of symmetry then graph the pre-image and the image.

Answer to Problem 33PPS

The coordinates of the vertices is $N^{\prime }\left(1,-2\right),P^{\prime }\left(5,-3\right),Q^{\prime }\left(5,-6\right),R^{\prime }\left(1,-6\right)$ and the graph of the image and the pre-image is shown in Figure 1

Explanation of Solution

Given:

The given vertices are $N\left(-2,-1\right),P\left(-3,-5\right),Q\left(-6,-5\right),R\left(-6,-1\right)$ .

The vertices are reflected about the $90°$ about the origin.

Calculation:

Consider the vertices of the image is,

  $N\left(-2,-1\right),P\left(-3,-5\right),Q\left(-6,-5\right),R\left(-6,-1\right)$

Multiply the vertex matrix by the matrix $\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$ as,

  $\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]\left[\begin{array}{cccc}-2& -3& -6& -6\\ -1& -5& -5& -1\end{array}\right]=\left[\begin{array}{cccc}1& 5& 5& 1\\ -2& -3& -6& -6\end{array}\right]$

Thus, the coordinate of the vertices of the image are $N^{\prime }\left(1,-2\right),P^{\prime }\left(5,-3\right),Q^{\prime }\left(5,-6\right),R^{\prime }\left(1,-6\right)$ .

The graph for the image and the pre-image is shown in Figure 1

  

Figure 1