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.

$$\begin{gathered} \therefore \mathrm{Coordinates}\mathrm{of}M=\left(\frac{2+4}{2},\frac{3-1}{2}\right) \\ =\left(3,1\right) \end{gathered}$$

The equation of the line parallel to 3x − 4y + 6 = 0 is $3x-4y+\lambda =0$

This line passes through M (3,1).

$$\begin{gathered} \therefore 9-4+\lambda =0 \\ \Rightarrow \lambda =-5 \end{gathered}$$

Substituting the value of $\lambda$ in $3x-4y+\lambda =0$, we get $3x-4y-5=0$, which is the equation of the required line.