Chapter 4.4, Problem 19PPS

To determine

To find: The coordinates of the vertices after the given dilation and then graph. Then determine the coordinates and the vertices of the image and graph the pre-image and the image.

Answer to Problem 19PPS

The coordinates of the vertices is $D^{\prime }\left(0,16\right),E^{\prime }8,F^{\prime }\left(0,0\right),G^{\prime }\left(-8,8\right)$ and the graph of the image and the pre-image is shown in Figure 1

Explanation of Solution

Given:

The given vertices are $D\left(0,4\right),E\left(2,2\right),F\left(0,0\right),G\left(-2,2\right)$ .

Calculation:

Consider the vertices of the triangle is,

  $D\left(0,4\right),E\left(2,2\right),F\left(0,0\right),G\left(-2,2\right)$

Multiply the vertex matrix by the scale factor $4$ as,

  $4\left[\begin{array}{cccc}0& 2& 0& -2\\ 4& 2& 0& 2\end{array}\right]=\left[\begin{array}{cccc}0& 8& 0& -8\\ 16& 8& 0& 8\end{array}\right]$

Thus, the coordinate of the vertices of the image is $D^{\prime }\left(0,16\right),E^{\prime }8,F^{\prime }\left(0,0\right),G^{\prime }\left(-8,8\right)$ .

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

  

Figure 1