Chapter 4.4, Problem 22PPS

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 22PPS

The coordinates of the vertices is $A^{\prime }\left(-9,-10\right),B^{\prime }\left(5,-6\right),C^{\prime }\left(-7,7\right)$ and the graph of the image and the pre-image is shown in Figure 1

Explanation of Solution

Given:

The given vertices are $A\left(9,-10\right),B\left(-5,-6\right),C\left(7,7\right)$ .

Calculation:

Consider the vertices of the image is,

  $A\left(9,-10\right),B\left(-5,-6\right),C\left(7,7\right)$

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

  $\left[\begin{array}{cc}-1& 0\\ 0& 1\end{array}\right]\left[\begin{array}{ccc}9& -5& 7\\ -10& -6& 7\end{array}\right]=\left[\begin{array}{ccc}-9& -5& -7\\ -10& -6& 7\end{array}\right]$

Thus, the coordinate of the vertices of the image is $A^{\prime }\left(-9,-10\right),B^{\prime }\left(5,-6\right),C^{\prime }\left(-7,7\right)$ .

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

  

Figure 1