show that a (_ 3,2) b (-5,-5) c(2,-3) d (-3,2) are the vertices of rhombus
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11th
Maths
Straight Lines
Introduction
Show that A(-3,2),B(-5,-5)...
MATHS
Show that A(−3,2),B(−5,−5),C(2,−3) and D(4,4) are the vertices of a rhombus.
November 22, 2019
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Vibhuti Arshan
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ANSWER
Consider ABCD be quadrilateral,
and we have given the points as: A(−3,2),B(−5,−5),C(2,−3) and D(4,4)
We know that all the sides of a rhombus are equal.
Therefore,
by distance formula we have,
Distance between two points =
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
⇒AB=
(−5+3)
2
+(−5−2)
2
=
4+49
=
53
⇒BC=
(2+5)
2
+(−3+5)
2
=
49+4
=
53
⇒CD=
(4−2)
2
+(4+3)
2
=
4+49
=
53
⇒AD=
(4+3)
2
+(4−2)
2
=
4+49
=
53
∴AB=BC=CD=AD
Therefore, ABCD is a rhombus (Proved)
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