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.

Answer 1

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.

`AB = sqrt((9-2)^2 + (1 - 0)^2)`

`= sqrt(49 + 1)`

`= sqrt50`

`BC= sqrt((11 - 9)^2 + (6 -1)^2)``

`= sqrt(4 + 25)`

`= sqrt29`

`CD = sqrt((11 - 4)^2 + (6 - 4)^2)`

`= sqrt(49 + 4)`

`= sqrt53`

`AD = sqrt((4- 5)^2 + (4 - 0)^2)`

`= sqrt(4 + 16)`

`= sqrty(20)`

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