Given triangle WXY with coordinates
[tex]W(3,4),X(12,10),Y(6,-2)[/tex]
The image W'X'Y' has coordinates
[tex]W^{\prime}(2,1),X^{\prime}(8,5),Y^{\prime}(4,-3)[/tex]
According to the image coordinates,the dilation is negative, the image has been translated downward also, therefore the scale factor and the translation unit is
[tex]\begin{gathered} \text{Dilation rule} \\ (x,y)\Rightarrow\frac{1}{k}(x^{\prime},y^{\prime}) \end{gathered}[/tex][tex]\begin{gathered} W(3,2)\Rightarrow W^{\prime}(\frac{2}{k},\frac{1}{k}) \\ \text{Hence } \\ \frac{2}{k}=3 \\ 3k=2 \\ k=\frac{2}{3} \end{gathered}[/tex][tex]\begin{gathered} \text{the dowward shift } \\ W^{\prime}(x^{\prime},y^{\prime}+h)\Rightarrow(8,5+h)\Rightarrow(\frac{2}{3}(12,10) \\ \text{Thus} \\ 5+h=\frac{20}{3} \\ h=\frac{20}{3}-5=\frac{20-15}{3}=\frac{5}{3} \end{gathered}[/tex]
Therefore the general rule is
[tex]\frac{2}{3}(x,y-\frac{5}{3})\Rightarrow(x^{\prime},y^{\prime}_{})[/tex]
Hence, the scale factor is 2/3
