Find the equation to the straight line parallel to `3x-4y+6=0\ ` and passing through the middle point of the joint of points (2,3), and (4,-1).

Explanation

Let the Given points be `A (2, 3) and B (4, − 1)`.


Let M be the midpoint of AB. ∴ Coordinates of `M = (2+4)/2,(3−1)/2 = (3,1)`


The equation of the line parallel to `3x − 4y + 6 = 0 is 3x – 4y + λ = 0`


This line passes through M (3, 1).

`∴ 9 – 4 + λ = 0 ⇒ λ = -5`
Substituting the value of λ in `3x – 4y + λ = 0`, we get `3x – 4y – 5 = 0`
Hence, the equation of the required line is `3x – 4y – 5 = 0.`