The line x=c cuts the triangle with corners (0,0)(1,1) and (9,1) into two regions. For the area of the two regions to be the same c must be equal to
(A) 5/2
(B)3
(C) 7/2
(D) 3 or 15
Answers
Answered by
3
Answer:
Correct answer is option 'B'.
Step-by-step explanation:
Answered by
1
Step-by-step explanation:
SlopeAC=
9
1
slope
y=
9
1
x
AB→y=x
A
1
=∫
0
1
(x−
9
x
)dx+∫
1
c
(1−
9
x
)dx
[
2
x
2
−
10
x
2
]
0
1
+[x−
18
x
2
]
1
c
=[
18
8x
2
]
0
1
+[x−
10
x
2
]
1
c
=[
9
4x
2
]
0
1
+[x−
10
x
2
]
1
c
=
9
4
+c−
10
c
2
−1+
18
1
=
16
8
+
18
1
−1+c−
18
c
2
=c−
18
c
2
−
2
1
A
2
=∫
c
9
(1−
9
x
)dx=[x−
10
x
2
]
c
9
=9−
18
81
−c+
18
c
2
=9−
2
9
+
18
c
2
−c
2x−
18
2c
2
=
2
9
+
2
1
=5
c
2
−18c+45=0
c
2
−15c−3c+45=0
c=3,15
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