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.

\[\therefore \text { Coordinates of C } = \left( \frac{1 + 3}{2}, \frac{3 + 1}{2} \right)\]

                                      \[ = \left( 2, 2 \right)\]

\[\text { Slope of AB } = \frac{1 - 3}{3 - 1} = - 1\]

\[ \therefore \text { Slope of the perpendicular bisector  of AB }= 1\]

Thus, the equation of the perpendicular bisector of AB is

\[y - 2 = 1\left( x - 2 \right)\]

\[ \Rightarrow x - y = 0\]

or, y=x