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Difference between revisions of "2006 AMC 12A Problems/Problem 11"
(Added solution)
Line 6: Line 6:
  
 
== Solution ==
 
== Solution ==
 +
<math> (x+y)^2 = x^2 + y^2 </math>
  
 +
<math> x^2 + 2xy + y^2 = x^2 + y^2 </math>
 +
 +
<math> 2xy = 0 </math>
 +
 +
Either:
 +
 +
<math> x = 0 </math>
 +
 +
or
 +
 +
<math> y = 0 </math>
 +
 +
This describes 2 lines <math> \Rightarrow C </math>
 
== See also ==
 
== See also ==
 
* [[2006 AMC 12A Problems]]
 
* [[2006 AMC 12A Problems]]

Revision as of 22:39, 11 July 2006

Problem

Which of the following describes the graph of the equation $(x+y)^2=x^2+y^2$?

$\mathrm{(A) \ } \;\mathrm{the\; empty\; set}\;\qquad \mathrm{(B) \ } \;\mathrm{one\; point}$$\mathrm{(C) \ } \;\mathrm{two\; lines}\;\qquad \mathrm{(D) \ } \;\mathrm{a\; circle}$$\mathrm{(E) \ } \;\mathrm{the\; entire \; plane}\;$

Solution

$(x+y)^2 = x^2 + y^2$

$x^2 + 2xy + y^2 = x^2 + y^2$

$2xy = 0$

Either:

$x = 0$

or

$y = 0$

This describes 2 lines $\Rightarrow C$

See also

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