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Byju's Answer
Standard XII
Mathematics
Distance Formula
Examine wheth...
Question
Examine whether the following points taken in order form a rectangle.
(-1, 1), (0, 0), (3, 3) and (2, 4)
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Solution
Let us consider the given points as
A
(
−
1
,
1
)
;
B
(
0
,
0
)
;
C
(
3
,
3
)
;
D
(
2
,
4
)
.
The distance between
A
B
=
√
(
−
1
−
0
)
2
+
(
1
−
0
)
2
=
√
1
+
1
=
√
2
The distance between
B
C
=
√
(
0
−
3
)
2
+
(
0
−
3
)
2
=
√
9
+
9
=
√
18
The distance between
C
D
=
√
(
3
−
2
)
2
+
(
3
−
4
)
2
=
√
1
+
1
=
√
2
The distance between
D
A
=
√
(
2
+
1
)
2
+
(
4
−
1
)
2
=
√
9
+
9
=
√
18
The distance between
A
C
=
√
(
−
1
−
3
)
2
+
(
1
−
3
)
2
=
√
(
−
4
)
2
+
(
−
2
)
2
=
√
16
+
4
=
√
20
The distance between
B
D
=
√
(
0
−
2
)
2
+
(
0
−
4
)
2
=
√
4
+
16
=
√
20
As the opposite sides
A
B
=
C
D
and
B
C
=
D
A
and the diagonals
A
C
=
B
D
.
Therefore, the quadrilateral which is formed by the points
A
,
B
,
C
,
D
is a rectangle.
Hence, this is the answer.
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