Difference between revisions of "2003 AMC 12A Problems/Problem 9"
Mathgeek2006 (talk | contribs) m (→Problem) |
|||
Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
− | A set <math>S</math> of points in the <math>xy</math>-plane is symmetric about the | + | A set <math>S</math> of points in the <math>xy</math>-plane is symmetric about the origin, both coordinate axes, and the line <math>y=x</math>. If <math>(2,3)</math> is in <math>S</math>, what is the smallest number of points in <math>S</math>? |
<math> \mathrm{(A) \ } 1\qquad \mathrm{(B) \ } 2\qquad \mathrm{(C) \ } 4\qquad \mathrm{(D) \ } 8\qquad \mathrm{(E) \ } 16 </math> | <math> \mathrm{(A) \ } 1\qquad \mathrm{(B) \ } 2\qquad \mathrm{(C) \ } 4\qquad \mathrm{(D) \ } 8\qquad \mathrm{(E) \ } 16 </math> |
Latest revision as of 20:35, 30 December 2014
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 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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.