Question

Find an equation of the perpendicular bisector of the line segment whose endpoints are given.

Answer 1

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

             $(\frac{x_{1}+x_{2} }{2} , \frac{y_{1}+y_{2} }{2} )$

             (-5 , 3)

The Slope of the line

 m =        $\frac{y_{2} -y_{1} }{x_{2}-x_{1} } = \frac{5-1}{-10} = \frac{-2}{5}$

The perpendicular slope

    =   $\frac{-1}{m} = \frac{-1}{\frac{-2}{5} } = \frac{5}{2}$

The equation of the perpendicular bisector line

 $y - y_{1} = m (x - x_{1} )$

 $y - 3 = \frac{5}{2} ( x-(-5))$

  2 y - 6 = 5( x +5)

    5 x + 25 -2y +6 =0

   5 x - 2 y + 31 =0