Perpendicular bisector

Find the perpendicular bisector of the segment $AB$ with $A(-1, 0)$ and $B(3, 2)$. First the midpoint $M$ is $\left( \dfrac{-1 + 3}{2}, \dfrac{0 + 2}{2} \right) = (1, 1)$.

The slope of $AB$ is $\dfrac{2 - 0}{3 - (-1)} = \dfrac{1}{2}$, so the perpendicular slope is $-2$. Passing through $M(1, 1)$, the line is $y - 1 = -2(x - 1)$, that is $y = -2x + 3$. Every point on this line is equidistant from $A$ and $B$. The large dots mark $A$, $B$, and the midpoint $M$.