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

Solution (By Examveda Team)

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