find the equation of the perpendicular bisector of the line segment joining the points (3,8) and (-5,6).​

Answer:y = - 4x + 3Step-by-step explanation:The perpendicular bisector is positioned at the midpoint of AB at right angles.We require to find the midpoint and slope m of ABCalculate m using the slope formulam = (y₂ - y₁ ) / (x₂ - x₁ )with (x₁, y₁ ) = A(3, 8) and (x₂, y₂ ) = B(- 5, 6)m = [tex]\frac{6-8}{-5-3}[/tex] = [tex]\frac{-2}{-8}[/tex] = [tex]\frac{1}{4}[/tex]Given a line with slope m then the slope of a line perpendicular to it is[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{4} }[/tex] = - 4mid point  = [0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]Using the coordinates of A and B, thenmidpoint AB = [0.5(3 - 5), 0.5(8 + 6) ] = (- 1, 7 )Equation of perpendicular in slope- intercept formy = mx + c ( m is the slope and c the y- intercept )with m = - 4y = - 4x + c ← is the partial equationTo find c substitute (- 1, 7) into the partial equationUsing (- 1, 7), then7 = 4 + c ⇒ c = 7 - 4 = 3y = - 4x + 3 ← equation of perpendicular bisector