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Mathematics
Mathematics
Problem
Consider
△
P
Q
R
\triangle PQR
△
P
QR
with vertices
P
(
1
,
2
)
P(1,2)
P
(
1
,
2
)
,
Q
(
4
,
−
1
)
Q(4,-1)
Q
(
4
,
−
1
)
and
R
(
3
,
5
)
R(3,5)
R
(
3
,
5
)
. Another triangle
△
P
′
Q
′
R
′
\triangle P'Q'R'
△
P
′
Q
′
R
′
has vertices
P
′
(
2
,
4
)
P'(2,4)
P
′
(
2
,
4
)
,
Q
′
(
8
,
−
2
)
Q'(8,-2)
Q
′
(
8
,
−
2
)
and
R
′
(
6
,
10
)
R'(6,10)
R
′
(
6
,
10
)
. The ratio of the areas
[
△
P
′
Q
′
R
′
]
:
[
△
P
Q
R
]
[\triangle P'Q'R']:[\triangle PQR]
[
△
P
′
Q
′
R
′
]
:
[
△
P
QR
]
equals a)
2
:
1
2:1
2
:
1
b)
4
:
1
4:1
4
:
1
c)
1
:
4
1:4
1
:
4
d)
8
:
1
8:1
8
:
1
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