Find the equation of the perpendicular bisector of the line joining th

1.	Find the equation of the perpendicular bisector of the line joining the points (1, 3) and (3, 1).
Answer» Given: A (1, 3) and B (3, 1) be the points joining the perpendicular bisector Let C be the midpoint of AB. So, coordinates of C = [(1+3)/2, (3+1)/2] = (2, 2) Slope of AB = [(1-3) / (3-1)] = -1 Slope of the perpendicular bisector of AB = 1 Thus, the equation of the perpendicular bisector of AB is given as, y – 2 = 1(x – 2) y = x x – y = 0 ∴ The required equation is y = x.

Find the equation of the perpendicular bisector of the line joining the points (1, 3) and (3, 1).

Answer»

Given:

A (1, 3) and B (3, 1) be the points joining the perpendicular bisector

Let C be the midpoint of AB.

So, coordinates of C = [(1+3)/2, (3+1)/2]

= (2, 2)
Slope of AB = [(1-3) / (3-1)]

= -1
Slope of the perpendicular bisector of AB = 1

Thus, the equation of the perpendicular bisector of AB is given as,

y – 2 = 1(x – 2)

y = x

x – y = 0

∴ The required equation is y = x.