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Mathematics
Problem
Let
A
(
1
,
2
)
A(1,2)
A
(
1
,
2
)
,
B
(
5
,
6
)
B(5,6)
B
(
5
,
6
)
and
C
(
2
,
1
)
C(2,1)
C
(
2
,
1
)
. Define point
D
D
D
by the relation
D
⃗
=
2
C
⃗
−
A
⃗
\vec{D}=2\vec{C}-\vec{A}
D
=
2
C
−
A
. Find the ratio of the areas
[
△
A
B
D
]
:
[
△
A
B
C
]
[\triangle ABD]:[\triangle ABC]
[
△
A
B
D
]
:
[
△
A
B
C
]
. a)
1
:
2
1:2
1
:
2
b)
2
:
1
2:1
2
:
1
c)
1
:
1
1:1
1
:
1
d)
3
:
2
3:2
3
:
2
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