Find the equation

Given: A (a, b) and B (a₁, b₁) be the given points

To find:

Equation of the right bisector of the line segment joining the points (a, b) and (a₁, b₁).

Explanation:

Let C be the midpoint of AB.

∴ coordinates of C

And, slope of AB

So, the slope of the right bisector of AB is

Thus, the equation of the right bisector of the line segment joining the points (a, b) and (a₁, b₁) is

⇒ 2 (a₁-a)x + 2y(b₁-b) + (a² + b²) – (a₁² + b₁²) = 0

Hence, equation of the required line 2 (a₁ – a)x + 2y(b₁- b) + (a² + b²) – (a₁² + b₁²) = 0