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Question: A coastal ecologist is determining the closest safe anchoring point for a research boat on a straight shoreline modeled by the line $y = 2x + 1$. Find the point on this line closest to the reef located at $(4, 1)$.
Solution: The shortest distance from a point to a line is along the perpendicular. The given line is $y = 2x + 1$, so slope $m = 2$. The perpendicular slope is $-
The line through $(4, 1)$ with slope $-

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