Question

Find the equation of the perpendicular bisector of the line segment whose end points are A(10, 4) and B(- 4, 9).

Answer 1

Perpendicular bisector: A perpendicular bisector is a line segment which is perpendicular to the given line segment and passes through its mid - point (or we can say bisects the line segment).

Now to find the equation of perpendicular bisector first, we will find mid - point of the given line using mid - point formula (call it midpoint as M),

Now we will calculate the slope of the given line and since lines are perpendicular, so the slope of two is related as m₁.m₂ = - 1.

Now the slope of perpendicular bisector is

m₁.m₂ = -1 ⇒ -5/14.m₂ = -1

m₂ = 14/5

Now equation of perpendicular bisector using two point form,

10y - 65 = 28x - 84

28x - 10y - 84 + 65 = 0

28x - 10y - 19 = 0

So, required equation of perpendicular bisector 28x - 10y - 19 = 0.