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).

Answer 1

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.