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Question
Show that A (−3, 2), B (−5, −5), C (2,−3), and D (4, 4) are the vertices of a rhombus.
Solution
Let A (−3, 2); B (−5,−5); C (2,−3) and D (4, 4) be the vertices of a quadrilateral. We have to prove that the quadrilateral ABCD is a rhombus.
So we should find the lengths of sides of quadrilateral ABCD.
`AB = sqrt((-5 + 3 )^2 + (-5-2)^2)`
`= sqrt(4 + 4 9)`
`= sqrt(53) `
`BC = sqrt((2 + 5 )^2 + (-3+ 5)^2)`
`= sqrt(4 + 4 9)`
`= sqrt(53) `
`CD = sqrt(( 4 - 2 )^2 + (4 +3)^2)`
`= sqrt(4 + 4 9)`
`= sqrt(53) `
`AD= sqrt((4 + 3 )^2 + (4-2)^2)`
`= sqrt(4 + 4 9)`
`= sqrt(53) `
All the sides of quadrilateral are equal. Hence ABCD is a rhombus.
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