What will be the equation of the perpendicular bisector of segment joining the points (5,-3) and (0,2)?

Let line $$l$$ perpendicularly bisects line joining  A(5,-3) and B(0,2) at C, thus C is the mid point of AB.

=> Coordinates of C = $$(\frac{5 + 0}{2} , \frac{-3 + 2}{2})$$

= $$(\frac{5}{2} , \frac{-1}{2})$$

Now, slope of AB = $$\frac{y_2 - y_1}{x_2 - x_1} = \frac{(2 + 3)}{(0 - 5)}$$

= $$\frac{5}{-5} = -1$$

Let slope of line $$l = m$$

Product of slopes of two perpendicular lines = -1

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

=> $$m = 1$$

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 $$l$$

=> $$(y + \frac{1}{2}) = 1(x - \frac{5}{2})$$

=> $$x - y = \frac{5}{2} + \frac{1}{2} = \frac{6}{2}$$

=> $$x - y = 3$$

=> Ans - (D)