show that the points (3,-2)(7,6)(-1,2)(-5,-6) from a rhombus
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Step-by-step explanation:
ANSWER
Consider the given points.
A(15,20),B(−3,12),C(−11,−6),D(7,2)
So,
AB=
(−3−15)
2
+(12−20)
2
AB=
(−18)
2
+(−8)
2
AB=
324+64
=
388
Similarly,
BC=
(−11+3)
2
+(−6−12)
2
BC=
(−8)
2
+(−18)
2
BC=
64+324
=
388
Similarly,
CD=
(7+11)
2
+(2+6)
2
CD=
(18)
2
+(8)
2
CD=
324+64
=
388
Similarly,
DA=
(15−7)
2
+(20−2)
2
DA=
(8)
2
+(18)
2
DA=
64+324
=
388
Therefore,
AB=BC=CD=AD
Now,
AC=
(−11−15)
2
+(−6−20)
2
AC=
(−26)
2
+(−26)
2
AC=
576+576
=
1152
Similarly,
BD=
(7+3)
2
+(2−12)
2
BD=
(10)
2
+(−10)
2
BD=
100+100
=
200
So,
AC
=BD
As all the sides are equal and diagonals are not equal.
Its shows that the following vertices are of rhombus.
Hence, this is the answer.
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