Chapter 4.4, Problem 7CYU

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 7CYU

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 $P\left(-1,2\right),Q\left(4,-4\right),R\left(-1,-4\right)$ .

Calculation:

Consider the vertices of the triangle is,

  $P\left(-1,2\right),Q\left(4,-4\right),R\left(-1,-4\right)$

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

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

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

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

  

Figure 1