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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.
`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.
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