# The points A(2, 0), B(9, 1) C(11, 6) and D(4, 4)

Question:

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

Solution:

Let A (2, 0); B (9, 1); C (11, 6) and D (4, 4) be the vertices of a quadrilateral. We have to check if the quadrilateral ABCD is a rhombus or not.

So we should find the lengths of sides of quadrilateral ABCD.

$\mathrm{AB}=\sqrt{(9-2)^{2}+(1-0)^{2}}$

$=\sqrt{49+1}$

$=\sqrt{50}$

$B C=\sqrt{(11-9)^{2}+(6-1)^{2}}$

$=\sqrt{4+25}$

$=\sqrt{29}$

$\mathrm{CD}=\sqrt{(11-4)^{2}+(6-4)^{2}}$

$=\sqrt{49+4}$

$=\sqrt{53}$

$\mathrm{AD}=\sqrt{(4-2)^{2}+(4-0)^{2}}$

$=\sqrt{4+16}$

$=\sqrt{20}$

All the sides of quadrilateral are unequal. Hence ABCD is not a rhombus.