Chapter 4.4, Problem 9CYU

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 9CYU

The coordinates of the vertices are $A^{\prime }\left(-1,-4\right),B^{\prime }\left(-4,-3\right),C^{\prime }\left(4,0\right),D^{\prime }\left(-1,1\right)$ and the figure for the image and the pre-image is shown in Figure 1

Explanation of Solution

Given:

The given vertices are $A\left(-4,1\right),B\left(-3,4\right),C\left(0,4\right),D\left(1,1\right)$ .

Calculation:

Consider the vertices of the triangle is,

  $A\left(-4,1\right),B\left(-3,4\right),C\left(0,4\right),D\left(1,1\right)$

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

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

Thus, the coordinate of the vertices of the image is $A^{\prime }\left(-1,-4\right),B^{\prime }\left(-4,-3\right),C^{\prime }\left(4,0\right),D^{\prime }\left(-1,1\right)$ .

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

  

Figure 1