Difference between revisions of "2003 AMC 12A Problems/Problem 9"
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== Solution == | == Solution == | ||
If <math>(2,3)</math> is in <math>S</math>, then <math>(3,2)</math> is also, and quickly we see that every point of the form <math>(\pm 2, \pm 3)</math> or <math>(\pm 3, \pm 2)</math> must be in <math>S</math>. Now note that these <math>8</math> points satisfy all of the symmetry conditions. Thus the answer is <math>D</math>. | If <math>(2,3)</math> is in <math>S</math>, then <math>(3,2)</math> is also, and quickly we see that every point of the form <math>(\pm 2, \pm 3)</math> or <math>(\pm 3, \pm 2)</math> must be in <math>S</math>. Now note that these <math>8</math> points satisfy all of the symmetry conditions. Thus the answer is <math>D</math>. | ||
+ | |||
+ | == See Also == | ||
+ | *[[2003 AMC 12A Problems]] | ||
+ | *[[2003 AMC 12A/Problem 8|Previous Problem]] | ||
+ | *[[2003 AMC 12A/Problem 10|Next Problem]] | ||
+ | |||
+ | [[Category:Introductory Algebra Problems]] |
Revision as of 10:46, 16 November 2008
Problem
A set of points in the
-plane is symmetric about the orgin, both coordinate axes, and the line
. If
is in
, what is the smallest number of points in
?
Solution
If is in
, then
is also, and quickly we see that every point of the form
or
must be in
. Now note that these
points satisfy all of the symmetry conditions. Thus the answer is
.