Chapter 12.7, Problem 7E

To determine

To graph: draw a polygon

Explanation of Solution

Given information: the vertices of polygon are $P\left(-6,2\right),Q\left(2,2\right)\text{ ,R}\left(2,0\right)\text{ and S}\left(-6,0\right)$ and the scale factor is $0.5$

Graph: first draw a polygon with the vertices $P\left(-6,2\right),Q\left(2,2\right)\text{ ,R}\left(2,0\right)\text{ and S}\left(-6,0\right)$ and then to dilate the polygon $PQRS$ ,multiply $x$ and $y$ coordinates of each vertices by $0.5$

Original	Image
$(x,y)$	$\left(0.5x,0.5y\right)$
$P(-6,2)$	$A(-3,1)$
$Q\left(2,2\right)$	$B(1,1)$
$R\left(2,0\right)$	$C(1,0)$
$S\left(-6,0\right)$	$D\left(-3,0\right)$

Finally draw a polygon $ABCD$ , as shown below

Interpretation: Hence, the vertices of image after dilation are $A\left(-3,1\right),B\left(1,1\right)\text{ ,C}\left(1,0\right)\text{ and D}\left(-3,0\right)$