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Byju's Answer
Standard X
Mathematics
Distance Formula
Three vertice...
Question
Three vertices of a parallelogram
A
B
C
D
taken in order are
A
(
3
,
6
)
,
B
(
5
,
10
)
and
C
(
3
,
2
)
the coordinate of the fourth vertex
D
.
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Solution
The coordinate of fourth point be
(
x
,
y
)
.
Given three coordinates of parallelogram-
A
(
3
,
6
)
B
(
5
,
10
)
C
(
3
,
2
)
Now,
Mid-point of
A
C
will be equal to mid-point of
B
D
.
Therefore,
Mid-point of
A
C
=
(
3
+
3
2
,
6
+
2
2
)
=
(
3
,
4
)
Mid-point of
B
D
=
(
x
+
5
2
,
y
+
10
2
)
Now,
x
+
5
2
=
3
⇒
x
=
1
y
+
10
2
=
4
⇒
y
=
−
2
Hence the coordinate of fourth point will be
(
1
,
−
2
)
.
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