Difference between revisions of "2012 AMC 10B Problems/Problem 3"
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<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> | ||
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| + | == Solution == | ||
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| + | 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 may 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). Answer choice B is correct. | ||
Revision as of 17:25, 26 February 2012
Problem
The point in the 
-plane with coordinates (1000, 2012) is reflected across the line 
. What are the coordinates of the reflected point?
Solution
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 may 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). Answer choice B is correct.
