Answer:
From the given graph:
the coordinates of triangle RST are;
R= (2, 1),
S= (2,-2),
T= (-1,-2)
Given: Scale factor = [tex]\frac{5}{3}[/tex] and center of dilation at (2,2)
The mapping rule for the dilation applied to the triangle as shown below:
[tex](x,y) \rightarrow (\frac{5}{3}(x-2)+2 , \frac{5}{3}(y-2)+2 )[/tex]; where k represents the scale factor i.e, [tex]k=\frac{5}{3}[/tex] or we can write it as ;
For R=(2, 1)
The image R' = [tex](\frac{5}{3}(2-2)+2 , \frac{5}{3}(1-2)+2 )[/tex]
⇒ R'= [tex](2, \frac{1}{3})[/tex]
Similarly for S= (2, -2) and T= (-1,-2)
therefore, the image of S'= [tex](\frac{5}{3}(2-2)+2 , \frac{5}{3}(-2-2)+2 )[/tex]
⇒ S'= [tex](2, \frac{-14}{3})[/tex]
The image of T' =[tex](\frac{5}{3}(-1-2)+2 , \frac{5}{3}(-2-2)+2 )[/tex]
⇒T' = [tex](-3, \frac{-14}{3})[/tex]
Now, labelling the image of triangle R'S'T' as shown in the figure given below
