2000 AIME I Problems/Problem 2
Problem
Let and
be integers satisfying
. Let
, let
be the reflection of
across the line
, let
be the reflection of
across the y-axis, let
be the reflection of
across the x-axis, and let
be the reflection of
across the y-axis. The area of pentagon
is
. Find
.
Solution
Since , we can find the coordinates of the other points:
,
,
,
. If we graph those points, we notice that since the latter four points are all reflected across the x/y-axis, they form a rectangle, and
is a triangle. The area of
is
and the area of
is
. Adding these together, we get
. Since
are positive,
, and by matching factors we get either
or
. Since
the latter case is the answer, and
.
See also
2000 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 1 |
Followed by Problem 3 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |