Find equation of the perpendicular bisector of segment joining the points (2,-5) and (0,7)?

Let line $$l$$ perpendicularly bisects line joining  A(2,-5) and B(0,7) at C, thus C is the mid point of AB.

=> Coordinates of C = $$(\frac{2 + 0}{2} , \frac{-5 + 7}{2})$$

= $$(\frac{2}{2} , \frac{2}{2}) = (1,1)$$

Now, slope of AB = $$\frac{y_2 - y_1}{x_2 - x_1} = \frac{(7 + 5)}{(0 - 2)}$$

= $$\frac{12}{-2} = -6$$

Let slope of line $$l = m$$

Product of slopes of two perpendicular lines = -1

=> $$m \times -6 = -1$$

=> $$m = \frac{1}{6}$$

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 $$l$$

=> $$(y - 1) = \frac{1}{6}(x - 1)$$

=> $$6y - 6 = x - 1$$

=> $$x - 6y = 1 - 6 = -5$$

=> Ans - (C)