A (-1, 1), B (5, 3) are opposite vertices of a square. The equation of the other diagonal ( not passing through A, B) of the square is

Let  A (-1 , 1)  B  (5, 3)

P = Mid point of AB

$\begin{array}{l}=\left(\frac{5-1}{2},\frac{3+1}{2}\right)\\ =\left(2,2\right)=\left(x_1,y_1\right)\end{array}$

$\begin{array}{l}Slopeof\overline{AB}=\frac{3-1}{5+1}=\frac{2}{6}=\frac{1}{3}\\ \overline{AB}\perp \overline{CD}\Rightarrow m=Slopeof\overline{CD}=\frac{-1}{Slopeof\overline{AB}}=-3\end{array}$

$\begin{array}{l}Equationof\overline{CD}isy-y_1=m\left(x-x_1\right)\\ \Rightarrow y-2=-3\left(x-2\right)\\ \Rightarrow y-2=-3x+6\\ \Rightarrow 3x+y-8=0\end{array}$