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Byju's Answer
Standard X
Mathematics
Collinearity Condition
Show that the...
Question
Show that the following point taken in order form the vertices of a rhombus.
(2, -3), (6, 5), (-2, 1) and (-6, -7)
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Solution
Consider the given points.
A
(
2
,
−
3
)
,
B
(
6
,
5
)
,
C
(
−
2
,
1
)
,
D
(
−
6
,
−
7
)
So,
A
B
=
√
(
6
−
2
)
2
+
(
5
+
3
)
2
A
B
=
√
(
4
)
2
+
(
8
)
2
A
B
=
√
16
+
64
=
√
80
Similarly,
B
C
=
√
(
−
2
−
6
)
2
+
(
1
−
5
)
2
B
C
=
√
(
−
8
)
2
+
(
−
4
)
2
B
C
=
√
64
+
16
=
√
80
Similarly,
C
D
=
√
(
−
6
+
2
)
2
+
(
−
7
−
1
)
2
C
D
=
√
(
−
4
)
2
+
(
−
8
)
2
C
D
=
√
16
+
64
=
√
80
Similarly,
D
A
=
√
(
2
+
6
)
2
+
(
−
3
+
7
)
2
D
A
=
√
(
8
)
2
+
(
4
)
2
D
A
=
√
64
+
16
=
√
80
Therefore,
A
B
=
B
C
=
C
D
=
A
D
Now,
A
C
=
√
(
−
2
−
2
)
2
+
(
1
+
3
)
2
A
C
=
√
(
−
4
)
2
+
(
4
)
2
A
C
=
√
16
+
16
=
√
32
Similarly,
B
D
=
√
(
−
6
−
6
)
2
+
(
−
7
−
5
)
2
B
D
=
√
(
−
12
)
2
+
(
−
12
)
2
B
D
=
√
144
+
144
=
√
288
So,
A
C
≠
B
D
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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