Answer:
y = 3x + 9
Step-by-step explanation:
The perpendicular bisector to the line segment is passing through the midpoint of the line segment. Coordinates of midpoint are ( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )
Formula of slope is m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Slopes of perpendicular lines are opposite reciprocals. So, if AB ⊥ CD , then [tex]m_{AB}[/tex] × [tex]m_{CD}[/tex] = - 1
y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )
~~~~~~~~~~~
(- 8, 5)
(4, 1)
m = ( 5 - 1) / ( - 8 - 4) = - [tex]\frac{1}{3}[/tex]
Opposite reciprocal to ( - [tex]\frac{1}{3}[/tex] ) is 3
Coordinates of midpoint are ( - 2 , 3 )
y - 3 = 3 ( x + 2 )
y = 3x + 9
