Find the equation of the right bisector of the line?

Question

The points A(-3,4) B(5,6)

Answer 1

Given line end points A(-3,4) B(5,6)

The line bisects AB at its mid point is perpendicular to it.

Let C be the mid point of AB

C = [ (-3+5)/2 , (4+6)/2 ] = [ 2/2 , 10/2 ] = [1 , 5]

Slope of line AB = m = (5-(-3))/(6-4) = 8/2 = 4

Required line slope m₁ = -1/m = -1/4

The line passes through (1,5) with slope -1/4 is

(y-5) = (-1/4)(x-1) ⇒ 4(y-5) = (-1)(x-1)

4y-20 = -x+1

x - 4y -21 = 0

Solution : The equation of the lie bisects points A(-3,4),B(5,6) is "x - 4y - 21 = 0"