check the picture below.
so we know S is the midpoint of PQ, and T is the midpoint of QR, thus
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&P&(~ -9 &,& 7~)
% (c,d)
&Q&(~ -3 &,& 7~)
\end{array}\quad
% coordinates of midpoint
\left(\cfrac{ x_2 + x_1}{2}\quad ,\quad \cfrac{ y_2 + y_1}{2} \right)
\\\\\\
S=\left( \cfrac{-3-9}{2}~,~\cfrac{7+7}{2} \right)\implies S=(-6,7)\\\\
-------------------------------[/tex]
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&Q&(~ -3 &,& 7~)
% (c,d)
&R&(~ -3 &,& 1~)
\end{array}
\\\\\\
T=\left(\cfrac{-3-3}{2}~,~\cfrac{1+7}{2} \right)\implies T=(-3,4)[/tex]
so, what's the distance from S to T?
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&S&(~ -6 &,& 7~)
% (c,d)
&T&(~ -3 &,& 4~)
\end{array}\\\\\\
% distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
ST=\sqrt{[-3-(-6)]^2+[4-7]^2}\implies ST=\sqrt{(-3+6)^2+(4-7)^2}
\\\\\\
ST=\sqrt{3^2+(-3)^2}\implies ST=\sqrt{18}\implies ST=\sqrt{9\cdot 2}
\\\\\\
ST=\sqrt{3^2\cdot 2}\implies ST=3\sqrt{2}[/tex]
