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 | ||
