Answer:
From the graph: we have the coordinates of RST i.e,
R = (2,1) , S = (2,-2) , T = (-1,-2)
Also, it is given the scale factor [tex]\frac{2}{3}[/tex] and center of dilation C (1,-1)
The mapping rule for the center of dilation applied for the triangle as shown below:
[tex](x, y) \rightarrow (\frac{2}{3}(x-1)+1, \frac{2}{3}(y+1)-1)[/tex]
or
[tex](x, y) \rightarrow (\frac{2}{3}x -\frac{2}{3}+1 , \frac{2}{3}y+\frac{2}{3}-1)[/tex]
or
[tex](x, y) \rightarrow (\frac{2}{3}x+\frac{1}{3} , \frac{2}{3}y-\frac{1}{3} )[/tex]
Now,
for R = (2,1)
the image R' = [tex](\frac{2}{3}(2)+\frac{1}{3} , \frac{2}{3}(1)-\frac{1}{3} )[/tex] or
[tex](\frac{4}{3}+\frac{1}{3} , \frac{2}{3}-\frac{1}{3} )[/tex]
⇒ R' = [tex](\frac{5}{3} , \frac{1}{3})[/tex]
For S = (2, -2) ,
the image S'= [tex](\frac{2}{3}(2)+\frac{1}{3} , \frac{2}{3}(-2)-\frac{1}{3} )[/tex] or
[tex](\frac{4}{3}+\frac{1}{3} , \frac{-4}{3}-\frac{1}{3} )[/tex]
⇒ S' = [tex](\frac{5}{3} , -\frac{5}{3})[/tex]
and For T = (-1, -2)
The image T' = [tex](\frac{2}{3}(-1)+\frac{1}{3} , \frac{2}{3}(-2)-\frac{1}{3} )[/tex] or
[tex](\frac{-2}{3}+\frac{1}{3} , \frac{-4}{3}-\frac{1}{3} )[/tex]
⇒ T' = [tex](\frac{-1}{3} , \frac{-5}{3})[/tex]
Now, label the image of RST on the graph as shown below in the attachment:
