Chapter 4.4, Problem 8CYU

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 8CYU

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

Explanation of Solution

Given:

The given vertices are $L\left(3,-5\right),M\left(1,2\right),N\left(3,3\right)$ .

The vertices are rotated $180°$ about the origin.

Calculation:

Consider the vertices of the image is,

  $L\left(3,-5\right),M\left(1,2\right),N\left(3,3\right)$

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

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

Thus, the coordinate of the vertices of the image is $L^{\prime }\left(3,-5\right),M^{\prime }\left(1,2\right),N^{\prime }\left(3,3\right)$ .

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

  

Figure 1