Question

# Write an equation of the perpendicular bisector of the segment with the endpoints A(-2,-2) and B(6,0).

Linear equations and graphs
Write an equation of the perpendicular bisector of the segment with the endpoints A(-2,-2) and B(6,0).

AB has a midpoint of $$\displaystyle{\left({\left(\frac{{-{2}+{6}}}{{2}}\right)},\frac{{-{2}+{6}}}{{2}}\right)}{)}{)}={\left({2},-{1}\right)}$$. The slope of AB is $$\displaystyle\frac{{{y}{2}-{y}{1}}}{{{x}{2}-{x}{1}}}=\frac{{{6}-{\left(-{2}\right)}}}{{{6}-{\left(-{2}\right)}}}=\frac{{2}}{{8}}=\frac{{1}}{{4}}$$ so the slope of its perpendicular bisector is -4. Using point slope form of a line, the equation of the perpendicular bisector of AB is: