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