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Byju's Answer
Standard XII
Mathematics
Distance Formula
The fourth ve...
Question
The fourth vertex
D
of a parallelogram
A
B
C
D
whose three vertices are
A
(
2
,
3
)
,
B
(
6
,
7
)
and
C
(
8
,
3
)
is
A
(
0
,
1
)
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B
(
0
,
−
1
)
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C
(
4
,
−
1
)
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D
(
−
1
,
4
)
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Solution
The correct option is
C
(
4
,
−
1
)
Let
A
(
2
,
3
)
,
B
(
6
,
7
)
and
C
(
8
,
3
)
be the vertices of parallelogra
And let
D
(
x
,
y
)
be the fourth vertex.
Midpoint of
A
C
=
(
2
+
8
2
,
3
+
3
2
)
=
(
5
,
3
)
Also, midpoint of
B
D
=
(
x
+
6
2
,
y
+
7
2
)
Since the diagonals of parallelogram bisect eachother at
O
Therefore, midpoint of
A
C
=
midpoint of
B
D
⇒
(
x
+
6
2
,
y
+
7
2
)
=
(
5
,
3
)
⇒
x
+
6
2
=
5
,
y
+
7
2
=
3
⇒
x
+
6
=
10
,
y
+
7
=
6
⇒
x
=
4
,
y
=
−
1
Therefore, the coordinates of the fourth vertex will be
(
x
,
y
)
=
(
4
,
−
1
)
.
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