# Math Help - show that a figure is a rhombus

1. ## show that a figure is a rhombus

Can anybody give me a hint what to do with this since there are no numbers given please.

Let P,Q,R,S are the vertices of a parallelogram. Show, by analytic geometry, that if the diagonals are perpendicular the figure is a rhombus.

thanks

2. Plot points at (0,0), (a,0), (b,c) and (a+b,c)

The slope of one diagonal is $\frac{c}{a+b}$, and the slope of the other diagonal is $\frac{c}{b-a}$.

Since the diagonals are perpendicular, $\frac{c}{a+b}=\frac{a-b}{c}$

Solving for $c$ yields $c^2=a^2-b^2$.

Now use the distance formula to show that two adjacent sides have the same length.

3. im working on it now sir! thanks.
God Bless