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smoked corn on the cob - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Find the point on the line \( 3x - 4y + 12 = 0 \) that is closest to the point \( (1, 2) \).

📌 The shortest distance from a point to a line is along the perpendicular from the point to the line.

📌 Given line: \( 3x - 4y + 12 = 0 \), and point \( P = (1, 2) \).

📌 The slope of the line: rewrite in slope-intercept form:

📌 3x + 12 = 4y \Rightarrow y = \frac{3}{4}x + 3

📌 So slope \( m = \frac{3}{4} \). The perpendicular slope is \( -\frac{4}{3} \).

📌 The line through \( (1, 2) \) with slope \( -\frac{4}{3} \) is:

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