Answer:
The equation of the perpendicular bisector line
5 x - 2 y + 31 =0
Step-by-step explanation:
Explanation:-
Given points are ( 0,1) and (-10,5)
The Midpoint of given two points
[tex](\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} )[/tex]
(-5 , 3)
The Slope of the line
m = [tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} } = \frac{5-1}{-10} = \frac{-2}{5}[/tex]
The perpendicular slope
= [tex]\frac{-1}{m} = \frac{-1}{\frac{-2}{5} } = \frac{5}{2}[/tex]
The equation of the perpendicular bisector line
[tex]y - y_{1} = m (x - x_{1} )[/tex]
[tex]y - 3 = \frac{5}{2} ( x-(-5))[/tex]
2 y - 6 = 5( x +5)
5 x + 25 -2y +6 =0
5 x - 2 y + 31 =0
