Mock AIME 4 2006-2007 Problems/Problem 2
Problem
Two points and
are chosen on the graph of
, with
. The points
and
trisect
, with
. Through
a horizontal line is drawn to cut the curve at
. Find
if
and
.
Solution
Since is the trisector of line segment
closer to
, the
-coordinate of
is equal to two thirds the
-coordinate of
plus one third the
-coordinate of
. Thus, point
has coordinates
for some
. Then the horizontal line through
has equation
, and this intersects the curve
at the point
, so
.