so that points A(-2,3), B(-4,-4), (13,-2), 0(5,5)
are the vertes Rombous A, B; C, D ?
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Answer:
ANSWER
AB=
(3−2)
2
+(4+1)
2
=
1+25
=
26
BC=
(−2−3)
2
+(3−4)
2
=
25+1
=
26
CD=
(−3+2)
2
+(−2−3)
2
=
1+25
=
26
DA=
(−3−2)
2
+(−2+1)
2
=
25+1
=
26
AC=
(−2−2)
2
+(3+1)
2
=
16+16
=
32
BD=
(−3−3)
2
+(−2−4)
2
=
36+36
=
72
Now we can see that
AB=BC=CD=DA=
26
units but daigonals AC
=BD
=> ABCD is a quadrilateral whose all sides are equal but diagonals are not equal.
=> ABCD is a rhombus, not a square.
Area of rhombus ABCD =
2
1
× (Product of diagonals)
=
2
1
×(AC×BD)
=
2
1
×(
3
2×
7
2)
=24 sq.units
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