Chapter 9.6, Problem 6CYU

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 6CYU

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

Explanation of Solution

The coordinates of the polygon are:

  $\begin{array}{c}Q\left(-4,4\right)\\ R\left(-4,-4\right)\\ S\left(4,-4\right)\\ T\left(4,4\right)\end{array}$

The graph of $\text{quad}QRST$ is shown below.

  

Figure (1)

Therefore, the magnification factor is $250$ .

The scale factor is $\frac{1}{2}$ .

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

  $\begin{array}{c}Q\left(-4,4\right)\to Q^{\prime }\left(-2,2\right)\\ R\left(-4,-4\right)\to R^{\prime }\left(-2,-2\right)\\ S\left(4,-4\right)\to S^{\prime }\left(2,-2\right)\\ T\left(4,4\right)\to T\left(2,2\right)\end{array}$

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

  

Figure (2)

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