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# The points A(-3, -4) and C(5, 4) are the ends of the diagonal of a rhombus ABCD. (a) Find the equation of the diagonal BD. (b) Given that the side BC has gradient $\frac{5}{3}$, find the coordinates of B and hence of D.

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The points $A(-3,4)$ and $C(5,4)$ are vertices of a rhombus $ABCD$. The goal of this task is to find the equation of the diagonal $BD$. In order to do so, use the fact that diagonals of a rhombus are perpendicular. Also, find the coordinates of $B$ and $D$ if it is known that the side $BD$ has gradient $\frac{5}{3}$. In order to do so, find the points of intersection of diagonals and sides of a rhombus.

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