Prove that the lines `2x+3y=19 and 2x+3y+7=0` are equidistant from the line `2x+3y=6`.

Explanation

Given,a lines` A, 2x + 3y = 19 `and` B, 2x + 3y + 7 = 0` also a line` C, 2x + 3y = 6`.

Let d1 be the distance between lines `2x + 3y = 19` and `2x + 3y = 6`, While `d_2` is the distance between lines` 2x + 3y + 7 = 0` and `2x + 3y = 6`

`d_1=(-19-(-6))/sqrt(2^2+3^2)=sqrt(13)`

`d2=(7-(-6))/(sqrt(2^2+3^2))=sqrt(13)`

Hence proved, the lines` 2x + 3y = 19` and `2x + 3y + 7 = 0` are equidistant from the line `2x + 3y = 6`