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

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== Problem ==
 
== Problem ==
  
The point in the <math>xy</math>-plane with coordinates (1000, 2012) is reflected across the line <math>y=2000</math>.  What are the coordinates of the reflected point?
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The point in the <math>xy</math>-plane with coordinates <math>(1000, 2012)</math> is reflected across the line <math>y=2000</math>.  What are the coordinates of the reflected point?
  
 
<math> \textbf{(A)}\ (998,2012)\qquad\textbf{(B)}\ (1000,1988)\qquad\textbf{(C)}\ (1000,2024)\qquad\textbf{(D)}\ (1000,4012)\qquad\textbf{(E)}\ (1012,2012) </math>
 
<math> \textbf{(A)}\ (998,2012)\qquad\textbf{(B)}\ (1000,1988)\qquad\textbf{(C)}\ (1000,2024)\qquad\textbf{(D)}\ (1000,4012)\qquad\textbf{(E)}\ (1012,2012) </math>

Latest revision as of 13:23, 19 August 2017

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 $(1000, 1988)$. $\boxed{\textbf{(B)}}$

See Also

2012 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 2
Followed by
Problem 4
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 10 Problems and Solutions

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