2013 AMC 12B Problems/Problem 8
Contents
Problem
Line has equation
and goes through
. Line
has equation
and meets line
at point
. Line
has positive slope, goes through point
, and meets
at point
. The area of
is
. What is the slope of
?
Solution
Line has the equation
when rearranged. Substituting
for
, we find that line
will meet this line at point
, which is point B. We call
the base and the altitude from A to the line connecting B and C,
, the height. The altitude has length
, and the area of
. Since
,
. Because
has positive slope, it will meet
to the right of
, and the point
to the right of
is
.
passes through
and
, and thus has slope
.
Video Solution
~Punxsutawney Phil or sugar_rush
See also
2013 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 7 |
Followed by Problem 9 |
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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