Chapter 12.7, Problem 3E

To determine

To graph: draw triangle $ABC$ with vertices $A\left(-2,0\right),B\left(1,1\right)\text{ and C}\left(2,-1\right)$ and also find the coordinates of the vertices of the image after a dilation having a scale factor of 4

Explanation of Solution

Given information: the coordinates of triangles ABC are as follows: $A\left(-2,0\right),B\left(1,1\right)\text{ and C}\left(2,-1\right)$

Graph: first draw triangle $ABC$ with vertices $A\left(-2,0\right),B\left(1,1\right)\text{ and C}\left(2,-1\right)$ then dilate $ABC$ ,multiply the $x$ and $y$ coordinates having a scale factor of 3

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

Finally draw a triangle $PQR$ , as shown below

Interpretation: Hence, the vertices of image after dilation are $P\left(-6,0\right),Q\left(3,3\right)\text{ and R}\left(6,-3\right)$