Chapter 4.4, Problem 4CYU

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 4CYU

The coordinates of the vertices are $D^{\prime }\left(-6,-3\right),E^{\prime }\left(0,9\right),F^{\prime }\left(6,-3\right)$ and the figure for the image and the pre-image is shown in Figure 1

Explanation of Solution

Given:

The given vertices are $D\left(-2,-1\right),E\left(0,3\right),F\left(2,-1\right)$ .

Calculation:

Consider the vertices of the triangle is,

  $D\left(-2,-1\right),E\left(0,3\right),F\left(2,-1\right)$

Multiply the vertex matrix by the scale factor $3$ as,

  $3\left[\begin{array}{ccc}-2& 0& 2\\ -1& 3& -1\end{array}\right]=\left[\begin{array}{ccc}6& 0& 6\\ -3& 9& -3\end{array}\right]$

Thus, the coordinate of the vertices of the image is $D^{\prime }\left(-6,-3\right),E^{\prime }\left(0,9\right),F^{\prime }\left(6,-3\right)$ .

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

  

Figure 1