show that show that the points - 4 - 7 - 12 - 85 and 54 take in order of vertical of a rhombus and finite area into area of rhombus is equal to 1
by 2 into product of its diagonals diagonals
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Explanation:
Let the points are A(−4,−7),B(−1,2),C(8,5),D(5,−4)
AB=
(−1−(−4))
2
+(2−(−7))
2
=
3
2
+9
2
=
90
=3
10
BC=
(8−(−1))
2
+(5−2)
2
=
9
2
+3
2
=
90
=3
10
CD=
(5−8)
2
+(−4−(5))
2
=
3
2
+9
2
=
90
=3
10
DA=
(−4−(5))
2
+(−7−(−4))
2
=
9
2
+3
2
=
90
=3
10
now ,
AC=
(8−(−4))
2
+(5−(−7))
2
=
(12)
2
+(12)
2
=
144
=12
2
BD=
(5−(−1))
2
+(−4−2)
2
=
6
2
+6
2
=
72
=6
2
Since , AB=CD=BC=DA,AC
=BD
so, it is rhombus.
Area of rhombus =
2
1
×12
2
×6
2
=72
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