Sides of a rhombus are parallel to the lines $x+y-1=0$ and $7x-y-5=0$. The diagonals of the rhombus intersect at $(1,3)$ and one of its vertices $A$ lies on the line $y=2x$. Find coordinates of vertex $A$.
We are given the slopes of the sides of rhombus. Then I assumed the lines as $y=7x+k$ and the other as $y=-x+j$. I could find the point of intersection, then it all became very absurd. Can you please suggest me any other more efficient and quick way? Geometrical answers are welcomed too.