Question

Find the equation of the right bisector of the line segment joining the points (3, 4) and (−1, 2).

Answer 1

Let the given points be A (3, 4) and B (−1, 2).
Let M be the midpoint of AB. 

\[\therefore \text { Coordinates of } M = \left( \frac{3 - 1}{2}, \frac{4 + 2}{2} \right) = \left( 1, 3 \right)\]

And, slope of AB = \[\frac{2 - 4}{- 1 - 3} = \frac{1}{2}\]

Let m be the slope of the right bisector of the line joining the points (3, 4) and (−1, 2).

\[\therefore m \times \text { Slope of } AB = - 1\]

\[ \Rightarrow m \times \frac{1}{2} = - 1\]

\[ \Rightarrow m = - 2\]

So, the equation of the line that passes through M (1, 3) and has slope −2 is

\[y - 3 = - 2\left( x - 1 \right) \]

\[ \Rightarrow 2x + y - 5 = 0\]

Hence, the equation of the right bisector of the line segment joining the points (3, 4) and (−1, 2) is \[2x + y - 5 = 0\].