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JEE Main 28 June 2022 Shift 2 Solved Paper
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© examsnet.com
Question : 12
Total: 90
Let a triangle be bounded by the lines
L
1
:
2
x
+
5
y
=
10
;
L
2
:
−
4
x
+
3
y
=
12
and the line
L
3
, which passes through the point
P
(
2
,
3
)
, intersects
L
2
at
A
and
L
1
at
B
. If the point
P
divides the line-segment
A
B
, internally in the ratio
1
:
3
, then the area of the triangle is equal to :
[28-Jun-2022-Shift-2]
110
13
132
13
142
13
151
13
Validate
Solution:
L
1
:
2
x
+
5
y
=
10
L
2
:
−
4
x
+
3
y
=
12
Solving
L
1
and
L
2
we get
C
≡
(
−
15
13
,
32
13
)
Now, Let
A
(
x
1
,
1
3
(
12
+
4
x
1
)
)
and
B
(
x
2
,
1
5
(
10
−
2
x
2
)
)
∴
3
x
1
+
x
2
4
=
2
and
(
12
+
4
x
1
)
+
10
−
2
x
2
5
4
=
3
So,
3
x
1
+
x
2
=
8
and
10
x
1
−
x
2
=
−
5
So,
(
x
1
,
x
2
)
=
(
3
13
,
95
13
)
A
=
(
3
13
,
56
13
)
and
B
=
(
95
13
,
−
12
13
)
=
|
1
2
(
3
13
(
−
44
13
)
−
56
13
(
110
13
)
+
1
(
2860
169
)
)
|
=
132
13
sq. units
© examsnet.com
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