Chapter 9.6, Problem 23PPS

To determine

To graph: The image of the polygon with the given vertices after a dilation centered at origin and given scale factor.

Answer to Problem 23PPS

The image of the polygon is shown in figure (2).

Explanation of Solution

The coordinates of the polygon are:

  $\begin{array}{l}A\left(9,9\right)\\ B\left(3,3\right)\\ C\left(6,0\right)\end{array}$

The graph of $\Delta ABC$ is shown below.

  

Figure (1)

The scale factor is $\frac{1}{3}$ .

The new coordinate are $\left(x,y\right)\to \left(kx,ky\right)$ . So,

  $\begin{array}{c}A\left(9,9\right)\to A^{\prime }\left(3,3\right)\\ B\left(3,3\right)\to B^{\prime }\left(1,1\right)\\ C\left(6,0\right)\to C^{\prime }\left(2,0\right)\end{array}$

The graph of the new triangle with old triangle is shown below.

  

Figure (2)

Therefore, the image of the polygon is shown in figure (2).