2009 AMC 12B Problems/Problem 9
Problem
Triangle has vertices
,
, and
, where
is on the line
. What is the area of
?
Solution
Solution 1
Because the line is parallel to
, the area of
is independent of the location of
on that line. Therefore it may be assumed that
is
. In that case the triangle has base
and altitude
, so its area is
.
Solution 2
The base of the triangle is . Its altitude is the distance between the point
and the parallel line
, which is
. Therefore its area is
. The answer is
.
Solution 3
By Shoelace, our area is:
We know
so we get:
See also
2009 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 8 |
Followed by Problem 10 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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