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
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
Plot points at (0,0), (a,0), (b,c) and (a+b,c)
The slope of one diagonal is $\displaystyle \frac{c}{a+b}$, and the slope of the other diagonal is $\displaystyle \frac{c}{b-a}$.
Since the diagonals are perpendicular, $\displaystyle \frac{c}{a+b}=\frac{a-b}{c}$
Solving for $\displaystyle c$ yields $\displaystyle c^2=a^2-b^2$.
Now use the distance formula to show that two adjacent sides have the same length.