Perpendicular bisector of a segment

Text

Find the perpendicular bisector of the segment with endpoints $A(1,2)$ and $B(7,6)$.

Solution

Midpoint: $M(4,4)$. Slope of $AB$: $\dfrac{6-2}{7-1}=\dfrac{2}{3}$, so the bisector has slope $-\dfrac{3}{2}$. $y-4=-\tfrac32(x-4)\Rightarrow y=-\tfrac32 x+10.$ $\boxed{\,y=-\tfrac32 x+10\,}$