2001 AIME II Problems/Problem 4
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Problem
Let . The lines whose equations are
and
contain points
and
, respectively, such that
is the midpoint of
. The length of
equals
, where
and
are relatively prime positive integers. Find
.
Solution
The coordinates of P can be written as and the coordinates of point Q can be written as
. By the midpoint formula, we have
and
. Solving for b gives
, so the point Q is
. The answer is twice the distance from Q to
, which by the distance formula is
. Thus, the answer is 67.
See also
2001 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |