Answer:
y = 6x + 12
Step-by-step explanation:
We require the midpoint M and slope of AB
Using the midpoint formula, then
M = [ [tex]\frac{1}{2}[/tex] (3 - 9) , [tex]\frac{1}{2}[/tex] (- 7 - 5) ] = (- 3, - 6 )
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = A(3, - 7) and (x₂, y₂ ) = B(- 9, - 5)
m = [tex]\frac{-5+7}{-9-3}[/tex] = [tex]\frac{2}{-12}[/tex] = - [tex]\frac{1}{6}[/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}{6} }[/tex] = 6
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 6 , thus
y = 6x + c ← is the partial equation
To find c substitute M(- 3, - 6) into the partial equation
- 6 = - 18 + c ⇒ c = - 6 + 18 = 12
y = 6x + 12 ← equation of perpendicular bisector
