2012 AMC 10B Problems/Problem 3

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.