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

Answer: Option D

$$\begin{array}{rl}& \text{O is mid point of AB}\\ & x=\frac{5+0}{2}=\frac{5}{2}\\ & y=\frac{-3+2}{2}=\frac{-1}{2}\\ & \text{Slope of AB }\left(m_1\right)\\ & =\frac{y_2-y_1}{x_2-x_1}\\ & =\frac{2-\left(-3\right)}{0-5}\\ & =\frac{5}{-5}\\ & =-1\end{array}$$
Slope of (m₂) CD = 1 [lines are perpendicular to each other]
m₁ × m₂ = -1
Equation of line
$$\begin{array}{rl}& \left(y+\frac{1}{2}\right)=1\left(x-\frac{5}{2}\right)\\ & \Rightarrow 2\left(x-y\right)=6\\ & \Rightarrow x-y=3\end{array}$$