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Question
Find the equation to the straight line parallel to 3x − 4y + 6 = 0 and passing through the middle point of the join of points (2, 3) and (4, −1).
Solution
Let the given points be A (2, 3) and B (4, −1). Let M be the midpoint of AB.
\[\therefore \text { Coordinates of M }= \left( \frac{2 + 4}{2}, \frac{3 - 1}{2} \right)\]
\[ = \left( 3, 1 \right)\]
The equation of the line parallel to 3x − 4y + 6 = 0 is \[3x - 4y + \lambda = 0\]
This line passes through M (3,1).
\[\therefore 9 - 4 + \lambda = 0\]
\[ \Rightarrow \lambda = - 5\]
Substituting the value of \[\lambda\] in \[3x - 4y + \lambda = 0\],we get
\[3x - 4y - 5 = 0\] ,which is the equation of the required line.
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