Find equation of the perpendicular bisector of segment joining the points (2,-6) and (4,0)?

Let line $$l$$ perpendicularly bisects line joining  A(2,-6) and B(4,0) at C, thus C is the mid point of AB.

=> Coordinates of C = $$(\frac{2 + 4}{2} , \frac{-6 + 0}{2})$$

= $$(\frac{6}{2} , \frac{-6}{2}) = (3,-3)$$

Now, slope of AB = $$\frac{y_2 - y_1}{x_2 - x_1} = \frac{(0 + 6)}{(4 - 2)}$$

= $$\frac{6}{2} = 3$$

Let slope of line $$l = m$$

Product of slopes of two perpendicular lines = -1

=> $$m \times 3 = -1$$

=> $$m = \frac{-1}{3}$$

Equation of a line passing through point $$(x_1,y_1)$$ and having slope $$m$$ is $$(y - y_1) = m(x - x_1)$$

$$\therefore$$ Equation of line $$l$$

=> $$(y + 3) = \frac{-1}{3}(x - 3)$$

=> $$3y + 9 = -x + 3$$

=> $$x + 3y = 3 - 9 = -6$$

=> Ans - (B)