Answer:
[tex]\frac{1}{5}[/tex]
Step-by-step explanation:
We want to find the scale factor of the dilation from ΔXYZ to ΔUVW.
The scale factor is given by the formula;
[tex]k=\frac{Image\:Length}{Corresponding\:Object\:Length}[/tex]
Since the dilation is from ΔXYZ to ΔUVW, our image triangle is ΔUVW.
We can now use any of the corresponding sides to determine the scale factor.
[tex]k=\frac{|UV|}{|XY|}[/tex]
[tex]\Rightarrow k=\frac{12}{60}[/tex]
We simplify to get;
[tex]\Rightarrow k=\frac{12}{12\times5}[/tex]
We cancel the common factors to get;
[tex]\Rightarrow k=\frac{1}{5}[/tex]
Therefore the scale factor is [tex]\frac{1}{5}[/tex]
