Chapter 4.4, Problem 6CYU

To determine

To find: The coordinates of the vertices of the image for each figure after the given translation and then graph the pre-image and the image.

Answer to Problem 6CYU

The coordinates of the vertices are $G^{\prime }\left(1,-5\right),H^{\prime }\left(3,-4\right),J^{\prime }\left(0,2\right),K^{\prime }\left(-2,1\right)$ and the figure for the image and the pre-image is shown in Figure 1

Explanation of Solution

Given:

The given vertices are $G\left(1,5\right),H\left(3,4\right),J\left(0,-2\right),K\left(-2,-1\right)$ .

Calculation:

Consider the vertices of the triangle is,

  $G\left(1,5\right),H\left(3,4\right),J\left(0,-2\right),K\left(-2,-1\right)$

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

  $\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]\left[\begin{array}{cccc}1& 3& 0& -2\\ 5& 4& -2& -1\end{array}\right]=\left[\begin{array}{cccc}1& 3& 0& -2\\ -5& -4& 2& 1\end{array}\right]$

Thus, the coordinate of the vertices of the image is $G^{\prime }\left(1,-5\right),H^{\prime }\left(3,-4\right),J^{\prime }\left(0,2\right),K^{\prime }\left(-2,1\right)$ .

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

  

Figure 1