Question

Find the equation of the perpendicular bisector of the line joining the points (1, 3) and (3, 1).

Answer 1

Let A (1, 3) and B (3, 1) be the given points.

Let C be the midpoint of AB.

$$\begin{gathered} \therefore \mathrm{Coordinates}\mathrm{of}C=\left(\frac{1+3}{2},\frac{3+1}{2}\right) \\ =\left(2,2\right) \end{gathered}$$

$$\begin{gathered} \mathrm{Slope}\mathrm{of}AB=\frac{1-3}{3-1}=-1 \\ \therefore \mathrm{Slope}\mathrm{of}\mathrm{the}\mathrm{perpendicular}\mathrm{bisector}\mathrm{of}AB=1 \end{gathered}$$

Thus, the equation of the perpendicular bisector of AB is

$$\begin{gathered} y-2=1\left(x-2\right) \\ \Rightarrow x-y=0 \end{gathered}$$
or, y=x