2007 AMC 12A Problems/Problem 13
Problem
A piece of cheese is located at in a coordinate plane. A mouse is at
and is running up the line
. At the point
the mouse starts getting farther from the cheese rather than closer to it. What is
?
Solution
We are trying to find the foot of a perpendicular from to
. Then the slope of the line that passes through the cheese and
is the negative reciprocal of the slope of the line, or
. Therefore, the line is
. The point where
and
intersect is
, and
.
See also
2007 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 12 |
Followed by Problem 14 |
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 |