Using analytical geometry, prove that the diagonals of a rhombus are perpendicular to each other.

Explanation

we need to prove ABCD is a rhombus

where AB=BC=BD=DA

A(0,0) B(S,0)

C(A+S,B) D(A,B)

`AD=sqrt(a^2+b^2)=s`

`a^2+b^2=s^2`

AB=`sqrt(s^2+0^2)=s`

BC=`sqrt((a+s-s)^2+(b-0)^2)=sqrt(a^2+b^2)=S`

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