Straight Lines And Pair Of Straight Lines

Let \(A(a, b), B(3,4)\) and \(C(-6,-8)\) respectively denote the centroid, circumcentre and orthocentre of a triangle. Then, the distance of the point \(P(2 a+3,7 b+5)\) from the line \(2 x+3 y-4=0\) measured parallel to the line \(x-2 y-1=0\) is