Chapter 4.4, Problem 25PPS

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 25PPS

The coordinates of the vertices is $L^{\prime }\left(-1,-2\right),M^{\prime }\left(5,-1\right),N^{\prime }\left(4,5\right),P^{\prime }\left(-2,-4\right)$ and the graph of the image and the pre-image is shown in Figure 1

Explanation of Solution

Given:

The given vertices are $L\left(1,-2\right),M\left(-5,-1\right),N\left(-4,5\right),P\left(2,4\right)$ .

The vertices are reflected about the $y$ axis.

Calculation:

Consider the vertices of the image is,

  $L\left(1,-2\right),M\left(-5,-1\right),N\left(-4,5\right),P\left(2,4\right)$

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

  $\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right]\left[\begin{array}{cccc}1& -5& -4& 2\\ -2& -1& 5& -4\end{array}\right]=\left[\begin{array}{cccc}-1& 5& 4& -2\\ -2& -1& 5& -4\end{array}\right]$

Thus, the coordinate of the vertices of the image is $L^{\prime }\left(-1,-2\right),M^{\prime }\left(5,-1\right),N^{\prime }\left(4,5\right),P^{\prime }\left(-2,-4\right)$ .

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

  

Figure 1