Question

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

(0,1) and (-10,5)
The equation is
andard form)

Answer 1

The equation of the perpendicular bisector line

5 x - 2 y + 31 =0

Explanation:

Explanation:-

Given points are ( 0,1) and (-10,5)

The Midpoint of given two points

`((x_(1)+x_(2) )/(2) , (y_(1)+y_(2) )/(2) )`

(-5 , 3)

The Slope of the line

m =
`(y_(2) -y_(1) )/(x_(2)-x_(1) ) = (5-1)/(-10) = (-2)/(5)`

The perpendicular slope

=
`(-1)/(m) = (-1)/((-2)/(5) ) = (5)/(2)`

The equation of the perpendicular bisector line

`y - y_(1) = m (x - x_(1) )`

`y - 3 = (5)/(2) ( x-(-5))`

2 y - 6 = 5( x +5)

5 x + 25 -2y +6 =0

5 x - 2 y + 31 =0