Since triangle STU is a reduction of the triangle PQR, their corresponding sides are related by the equation:
[tex]S_{\text{PQR}}=kS_{\text{STU}}[/tex]Where K is a constant, and that constant is the same whichever pair of corresponding sides we choose.
Let's take the PQR side, its length is given by:
[tex]\begin{gathered} P=(-8,4),R=(-4,-2) \\ \Rightarrow d_{PR}=\sqrt[]{(-8+4)^2+(4+2)^2}=\sqrt[]{16+36}=\sqrt[]{52} \end{gathered}[/tex]On the other hand, the length of the SU side is:
[tex]\begin{gathered} S=(-2,1),U\approx(-1,-1) \\ \Rightarrow d_{SU}\approx\sqrt[]{(-2+1)^2+(1+1)^2}=\sqrt[]{1+4}=\sqrt[]{5} \end{gathered}[/tex]Then, we need to find the value of c in the equation
[tex]\begin{gathered} d_{PR}=c\cdot d_{SU} \\ \Rightarrow c=\frac{d_{PR}}{d_{SU}}\approx\sqrt[]{\frac{52}{5}}=\sqrt[]{10.4}=3.22490\ldots \\ \Rightarrow c\approx3.225 \end{gathered}[/tex]Then, as STU is the reduction of PQR, the answer is 1/c, which is:
[tex]\begin{gathered} \frac{1}{c}\approx\frac{1}{\sqrt[]{10.4}}=0.310087 \\ \Rightarrow\frac{1}{c}\approx0.31 \end{gathered}[/tex]The reduction factor is approximately 0.31. For a better result, we need to know with more certainty the coordinates of U