2003 AMC 12A Problems/Problem 9
Problem
A set of points in the
-plane is symmetric about the origin, both coordinate axes, and the line
. If
is in
, what is the smallest number of points in
?
Solution
If is in
, then its reflection in the line
, i.e.
, is also in
. Now by reflecting these points in both coordinate axes, we quickly deduce that every point of the form
or
must be in
. Moreover, by drawing out this set of
points, we observe that it satisfies all of the required symmetry conditions, so no more points need to be added to
. Accordingly, the smallest possible number of points in
is precisely
.
See Also
2003 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 8 |
Followed by Problem 10 |
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 |
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