Find the equation of side $AB$ if point $A\equiv(-3,1) $, equation of median through $B,L_1:2x+y-3=0$ and angle bisector of angle $C,L_2:7x-4y-1=0$.
All I could think of was using the fact that reflection of $A$ in line $L_2$ lies on $BC$ but then we need $C$ to use it in order to find line $AC$ also we could use the fact that distance of $A$ and $B$ from $L_1$ along line AB would be equal but we don't know line $AB$.
Any hints or suggestions would be helpful.
Hint: Let $C$ be $\left(t, \dfrac{7t-1}{4}\right)$. The mid-point of $A,C$ lies on the median through $B$ and hence $t$ and $C$ are obtained. $B$ can be found on the lines you mentioned or you could consider:
Assume $B$ as $\left(t, 3-2t\right)$. Since you know the midpoint of $AC$, you have the centroid. You can also obtain centroid as the A.M of the vertices and thus obtain $t$