Chapter 4.4, Problem 18PPS

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 18PPS

The coordinates of the vertices is $T^{\prime }\left(-6,2\right),U^{\prime }\left(4,-2\right),V^{\prime }\left(2,-10\right)$ and the graph of the image and the pre-image is shown in Figure 1

Explanation of Solution

Given:

The given vertices are $T\left(-4,1\right),U\left(2,-1\right),V\left(1,-5\right)$ .

Calculation:

Consider the vertices of the triangle is,

  $T\left(-4,1\right),U\left(2,-1\right),V\left(1,-5\right)$

Consider the vertices are dialled so that the perimeter is twice the original perimeter.

Multiply the vertex matrix by the scale factor $2$ as,

  $2\left[\begin{array}{ccc}-3& 2& 1\\ -1& -1& -5\end{array}\right]=\left[\begin{array}{ccc}-6& 4& 2\\ -2& -2& -10\end{array}\right]$

Thus, the coordinate of the vertices of the image is $T^{\prime }\left(-6,2\right),U^{\prime }\left(4,-2\right),V^{\prime }\left(2,-10\right)$ .

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

  

Figure 1