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Home » So unless rate is not 120, contradiction. - Dachbleche24

So unless rate is not 120, contradiction. - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 5Question: Find the point on the line $ y = -\frac{1}{2}x + 5 $ that is closest to the point $ (4, 3) $, modeling the optimal meeting spot between two social cliques.

📌 Solution: The closest point on a line to a given point is the perpendicular projection. The slope of the line is $ m = -\frac{1}{2} $, so the perpendicular slope is $ 2 $. The equation of the perpendicular line through $ (4, 3) $ is $ y - 3 = 2(x - 4) $. Solving the system:

📌 y = -\frac{1}{2}x + 5 \\

📌 y = 2x - 5

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