2012 AMC 10B Problem 3

Notice that the line in question is perfectly horizontal. This means that if we were to construct a perpendicular line segment from the point to the line, to find the reflected coordinates of the point, we simply double the distance along that line segment. The line segment from $(1000,2012)$ to $y=2000$ is of length $12,$ so the reflected point is along this same line segment, but a distance of $12$ on the other side of the horizontal line. This yields $(1000,1988).$ Thus, the correct answer is B .