Chapter 12.7, Problem 8E

To determine

To graph: draw a polygon

Explanation of Solution

Given information: the vertices of polygon are $E\left(-8,4\right),F\left(4,4\right)\text{ ,}G\left(0,-4\right)\text{ and }H\left(-4,-4\right)$ and the scale factor is $\frac{1}{4}$

Graph: first draw a polygon with the vertices $E\left(-8,4\right),F\left(4,4\right)\text{ ,}G\left(0,-4\right)\text{ and }H\left(-4,-4\right)$ and then to dilate the polygon $EFGH$ ,multiply $x$ and $y$ coordinates of each vertices by $\frac{1}{4}$

Original	Image
$(x,y)$	$\left(\frac{1}{4}x,\frac{1}{4}y\right)$
$E(-8,4)$	$P(-2,1)$
$F\left(4,4\right)$	$Q(1,1)$
$G\left(0,-4\right)$	$R(0,-1)$
$H\left(-4,-4\right)$	$S\left(-1,-1\right)$

Finally draw a polygon $PQRS$ , as shown below

Interpretation: Hence, the vertices of image after dilation are $P\left(-2,1\right),Q\left(1,1\right)\text{,R}\left(0,-1\right)\text{ and }S\left(-1,-1\right)$