If the points A$(2,0)$, B$(9,1)$, C$(11,6)$ and D$(4,4)$ are the vertices of a quadrilateral ABCD. Then Determine whether ABCD is a rhombus or not.

Given that the points are A$(2,0)$, B$(9,1)$, C$(11,6)$ and D$(4,4)$.

Now Coordinates of mid-point of AC are

$(11+2/2,6+0/2)=(13/2,3)$

Coordinates of mid-point of BD are

$(9+4/2,1+4/2)=(13/2,5/2)$

As we know that the coordinates of the mid-point of AC ≠ coordinates of mid-point of BD, therefore ABCD is not even a parallelogram.

Hence, ABCD cannot be a rhombus too.