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Reflecting Point over Line

Source: 2012 AMC10B Problem #3

February 23, 2012
analytic geometryAMC

Problem Statement

The point in the xyxy-plane with coordinates (1000,2012)(1000,2012) is reflected across line y=2000y=2000. What are the coordinates of the reflected point?
<spanclass=′latex−bold′>(A)</span> (998,2012)<spanclass=′latex−bold′>(B)</span> (1000,1988)<spanclass=′latex−bold′>(C)</span> (1000,2024)<spanclass=′latex−bold′>(D)</span> (1000,4012)<spanclass=′latex−bold′>(E)</span> (1012,2012) <span class='latex-bold'>(A)</span>\ (998,2012) \qquad<span class='latex-bold'>(B)</span>\ (1000,1988)\qquad<span class='latex-bold'>(C)</span>\ (1000,2024)\qquad<span class='latex-bold'>(D)</span>\ (1000,4012)\qquad<span class='latex-bold'>(E)</span>\ (1012,2012)
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