Question

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

Answer 1

Let $A(x,0)$, $B(0,y)$, $C(-x,0)$ & $D(0,-y)$ be the vertices of the rhombus.

We can verify by distance formula that $AB=BC-CD=DA=\sqrt{x^2+y^2}$

AC & BD are diagonals of rhombus which intersect at 'O'.

Now, AC & BD are along x-axis & y-axis which are perpendicular to each other.

Thus, diagonals of a rhombus are perpendicular to each other.