Answer:
y = - 4x + 3
Step-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 AB
Calculate m using the slope formula
m = (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] = - 4
mid point = [0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]
Using the coordinates of A and B, then
midpoint AB = [0.5(3 - 5), 0.5(8 + 6) ] = (- 1, 7 )
Equation of perpendicular in slope- intercept form
y = mx + c ( m is the slope and c the y- intercept )
with m = - 4
y = - 4x + c ← is the partial equation
To find c substitute (- 1, 7) into the partial equation
Using (- 1, 7), then
7 = 4 + c ⇒ c = 7 - 4 = 3
y = - 4x + 3 ← equation of perpendicular bisector
