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>\boxed{\mathrm{(D)}\ 8}</math>. |
== See Also == | == See Also == | ||
− | + | {{AMC12 box|year=2003|ab=A|num-b=8|num-a=10}} | |
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[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] |
Revision as of 16:58, 31 July 2011
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 .
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 |