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Show that points A (-4, -7), B (-1,2) , ...

Show that points A (-4, -7), B (-1,2) , C (8,5) and D(5,-4)
are the vertices pf rhomus ABCD.

Text Solution

Verified by Experts

`A(-4,-7),B(-1,2),C(8,5)` and `D(5,-4)`.
By distance formula
`AB=sqrt([-1-(-4)]^(2)+[2-(-7)]^(2))`
`:.AB=sqrt((3)^(2)+9^(2))`
`:.AB=sqrt(9+81)`
`:.AB=sqrt(90)`
`:.AB=sqrt(9xx10)`
`:.AB=3sqrt(10)`………1
`BC=sqrt([8-(-1)]^(2)+(5-2)^(2))`
`:.BC=sqrt(9^(2)+3^(2))`
`:.BC=sqrt(81+9)`
`:.BC=sqrt(90)`
`:.BC=sqrt(9xx10)`
`:.BC=3sqrt(10)`
`CD=sqrt((5-8)^(2)+(-4-5)^(2))`
`:.CD=sqrt((-3)^(2)+(-9)^(2))`
`:.CD=sqrt(9+81)`
`:.CD=sqrt(90)`
`:.CD=sqrt(9xx10)`
`:.CD=3sqrt(10)`
`AD=sqrt([5-(-4)]^(2)+[-4-(-7)]^(2))`
`:.AD=sqrt(9^(2)+3^(2))`
`:.AD=sqrt(81+9)`
`:.AD=sqrt(90)`
`:.AD=sqrt(9xx10)`
`:.AD=3sqrt(10)`......4
`:.` from 1, 2, 3 and 4
`AB=BC=CD=AD`
`:.square ABCD` is a rhombus.
`A(-4,-7),B(-1,2),C(8,5)` and `D(5,-4)` are vertices of rhombus ABCD.
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