A1. Which of the following equations of lines is the equation of the perpendicular bisector of the segment with endpoints $A(3,-3)$ and $B(2,-2)$?
(A) $y=-x-3$
(B) $x+y-1=0$
(C) $x-y-5=0$
(D) $3 x-2 y=0$
(E) $\frac{x}{3}-\frac{y}{2}=1$
A1. The perpendicular bisector of the line segment $AB$ passes through the midpoint $S\left(\frac{5}{2},-\frac{5}{2}\right)$ of the line segment $AB$ and is perpendicular to the line segment $AB$. The slope of the line through points $A$ and $B$ is $k_{1}=\frac{-2-(-3)}{2-3}=-1$. Therefore, the slope of the perpendicular bisector is $k_{2}=-\frac{1}{k_{1}}=1$. Considering $y=kx+n$ or $-\frac{5}{2}=1 \cdot \frac{5}{2}+n$, we get $n=-5$. Thus, the equation of the perpendicular bisector of the line segment $AB$ is $y=x-5$ or $x-y-5=0$.