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Difference between revisions of "2012 AMC 10B Problems/Problem 3"

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== Solution ==
 
== Solution ==
  
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The line <math>y = 2000</math> is a horizontal line located <math>12</math> units beneath the point <math>(1000, 2012)</math>. When a point is reflected about a horizontal line, only the <math>y</math> - coordinate will change. The <math>x</math> - coordinate remains the same. Since the <math>y</math>-coordinate of the point is <math>12</math> units above the line of reflection, the new <math>y</math> - coordinate  will be <math>2000 - 12 = 1988</math>. Thus, the coordinates of the reflected point are <math>(1000, 1988)</math>. Answer choice <math>\boxed{B}</math> is correct.
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The line <math>y = 2000</math> is a horizontal line located <math>12</math> units beneath the point <math>(1000, 2012)</math>. When a point is reflected about a horizontal line, only the <math>y</math> - coordinate will change. The <math>x</math> - coordinate remains the same. Since the <math>y</math>-coordinate of the point is <math>12</math> units above the line of reflection, the new <math>y</math> - coordinate  will be <math>2000 - 12 = 1988</math>. Thus, the coordinates of the reflected point are <math>(1000, 1988)</math>. <math>\boxed{\textbf{(B)}}</math>

Revision as of 21:30, 17 February 2013

Problem

The point in the $xy$-plane with coordinates (1000, 2012) is reflected across the line $y=2000$. What are the coordinates of the reflected point?

$\textbf{(A)}\ (998,2012)\qquad\textbf{(B)}\ (1000,1988)\qquad\textbf{(C)}\ (1000,2024)\qquad\textbf{(D)}\ (1000,4012)\qquad\textbf{(E)}\ (1012,2012)$

Solution

The line $y = 2000$ is a horizontal line located $12$ units beneath the point $(1000, 2012)$. When a point is reflected about a horizontal line, only the $y$ - coordinate will change. The $x$ - coordinate remains the same. Since the $y$-coordinate of the point is $12$ units above the line of reflection, the new $y$ - coordinate will be $2000 - 12 = 1988$. Thus, the coordinates of the reflected point are $(1000, 1988)$. $\boxed{\textbf{(B)}}$

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