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