2012 AMC 10B Problems/Problem 3

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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2012 AMC 10B Problems/Problem 3

Problem

Solution