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

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

📅 March 11, 2026 👤 scraface
Mar 11, 2026
Find the point on the line \( 3x - 4y + 12 = 0 \) that is closest to the point \( (1, 2) \).

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📌 Solution: Compute $ 2\overrightarrow{OA} = \begin{bmatrix} 4 \\ 2 \end{bmatrix} $ and $ 3\overrightarrow{OB} = \begin{bmatrix} -3 \\ 9 \end{bmatrix} $. Subtract:
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📌 Then $v_2 = 6 + 2(-\frac{45}{14}) = \frac{84 - 90}{14} = -\frac{6}{14} = -\frac{3}{7}$, and $v_3 = 11 + 3(-\frac{45}{14}) = \frac{154 - 135}{14} = \frac{19}{14}$.
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