1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard X
Mathematics
Distance between Two Points on the Same Coordinate Axes
If the points...
Question
If the points
A
(
−
2
,
−
1
)
,
B
(
1
,
0
)
,
C
(
a
,
3
)
and
D
(
1
,
b
)
form a parallelogram
A
B
C
D
, find the value of
a
and
b
.
Open in App
Solution
In the parallelogram
A
B
C
D
,
A
C
and
B
D
are the diagonals.
Co-ordinates of mid-point of
A
C
=
(
−
2
+
a
2
,
1
+
1
2
)
Co-ordinate of mid-point of
B
D
=
(
1
+
1
2
,
0
+
b
2
)
It is known that diagonals of the parallelogram bisect each other. Thus mid point of
A
C
and
B
D
coincide each other.
Thus,
−
2
+
a
2
=
1
⟹
a
=
4
1
+
1
2
=
b
2
⟹
b
=
2
Suggest Corrections
0
Similar questions
Q.
If
A
(
−
2
,
1
)
,
B
(
1
,
0
)
,
C
(
x
,
3
)
and
D
(
1
,
y
)
are the vertices of parallelogram, then find the values of
x
and
y
.
Q.
(i) If the points A (a, −11), B (5, b), C(2, 15) and D (1, 1) are the vertices of a parallelogram ABCD, find the values of a and b.
(ii) Point A(3, 1), B(5, 1), C(a, b) and D(4, 3) are vertices of a parallelogram ABCD. Find the values of a and b.