$A\;(-3,-4) $ and $ C \; (5,4)$ are the ends of the diagonal of a rhombus $ABCD$.
Given that the side BC has gradient $\frac{5}{3}$; How could we find the coordinates of $B$ and hence of $D$?
Context
In a rhombus, both diagonals intersect at their midpoint. Therefore, it suffices to find $B$, from where $D$ can be found by using $B+D=A+C$. But how to find $B$? The slope of BC is known, but not its length.