217
You visited us
217
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Section Formula
Point A3,1, B...
Question
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.
Open in App
Solution
Given: Point A(3, 1), B(5, 1), C(a, b) and D(4, 3) are vertices of a parallelogram ABCD.
Diagonals of a parallelogram bisect each other.
∴ Mid point of AC = Mid point of BD
Mid
point
of
x
1
,
y
1
and
x
2
,
y
2
is
x
1
+
x
2
2
,
y
1
+
y
2
2
.
Mid
point
of
A
C
=
3
+
a
2
,
1
+
b
2
Mid
point
of
B
D
=
5
+
4
2
,
1
+
3
2
=
9
2
,
4
2
=
9
2
,
2
∴
3
+
a
2
,
1
+
b
2
=
9
2
,
2
⇒
3
+
a
2
=
9
2
and
1
+
b
2
=
2
⇒
3
+
a
=
9
and
1
+
b
=
4
⇒
a
=
6
and
b
=
3
Hence, the values of a and b is 6 and 3, respectively.
Suggest Corrections
65
Similar questions
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.