In a #DeltaXYZ# having #X(-3,2)#, #Y(-5,-6)# and #Z(-5,0)#, is perpendicular bisector of #YZ# same as median from #X#?
The equations are not the same.
Find the midpoint of YZ using the midpoint formula
Since YZ is a vertical line:
The perpendicular bisector is a horizontal line:
The median from X goes from
Equation of the median
Use either the midpoint or point X to find b:
Equation of the median:
Perpendicular bisector of
As the abscissa (i.e.
and as such its perpendicular bisector will be parallel to
As midpoint of
equation of perpendicular bisector is
and median from
Note it is different from the equation of median given in question.
Obviously perpendicular bisector of