The distance of a point \((2,5)\) from the line \(3 x+y+4=0\) measured along the line \(\mathrm{L}_1\) and \(\mathrm{L}_2\) are same. If slope of line \(L_1\) is \(\frac{3}{4}\), then slope of the line \(\mathrm{L}_2\) is

According to the given condition, in \(\triangle \mathrm{ABC}\), \(\mathrm{AB}=\mathrm{AC}\).
\(\therefore \quad \triangle \mathrm{ABC}\) is an isosceles triangle.
Let \(\mathrm{m}, \mathrm{m}_1, \mathrm{~m}_2\) be the slopes of given line, \(\mathrm{L}_1\) and \(\mathrm{L}_2\) respectively.
\(\begin{array}{ll}
\therefore & \mathrm{m}=-3, \mathrm{~m}_1=\frac{3}{4} \\
\therefore & \left|\frac{\mathrm{m}-\mathrm{m}_1}{1+\mathrm{mm}_1}\right|=\left|\frac{\mathrm{m}-\mathrm{m}_2}{1+\mathrm{mm}_2}\right| \\
\therefore & 3=\left|\frac{-3-\mathrm{m}_2}{1+3 \mathrm{~m}_2}\right| \\
& \Rightarrow \mathrm{m}_2=0
\end{array}\)