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Byju's Answer
Standard X
Mathematics
Area of a Triangle Given Its Vertices
Show that the...
Question
Show that the following points taken in order form the vertices of a parallelogram
(-7, -5), (-4, 3), (5, 6) and (2, -2)
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Solution
Let
A
,
B
,
C
and
D
represent the points
(
–
7
,
–
5
)
,
(
–
4
,
3
)
,
(
5
,
6
)
and
(
2
,
–
2
)
Distance of
A
B
A
B
=
√
(
–
4
+
7
)
2
+
(
3
+
5
)
2
A
B
=
√
3
2
+
8
2
A
B
=
√
9
+
64
A
B
=
√
73
Similarly
Distance of
B
C
B
C
=
√
(
5
+
4
)
2
+
(
6
−
3
)
2
B
C
=
√
9
2
+
3
2
B
C
=
√
81
+
9
B
C
=
√
90
Similarly
Distance of
C
D
C
D
=
√
(
2
−
5
)
2
+
(
−
2
−
6
)
2
C
D
=
√
(
−
3
)
2
+
(
−
8
)
2
C
D
=
√
9
+
64
C
D
=
√
73
Similarly
Distance of
D
A
D
A
=
√
(
−
7
−
2
)
2
+
(
−
5
+
2
)
2
D
A
=
√
(
−
9
)
2
+
(
−
3
)
2
D
A
=
√
81
+
9
D
A
=
√
90
So,
A
B
=
C
D
=
√
73
and
B
C
=
D
A
=
√
90
i.e., The opposite sides are equal.
Hence
A
B
C
D
is a parallelogram.
Suggest Corrections
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