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Triangle $ABC$ has vertices $A(2, 3),$ $B(1, -8)$ and $C(-3, 2).$ The line containing the altitude through $A$ intersects the point $(0, y).$ What is the value of $y$?

 May 10, 2024
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\(m_{BC } = \dfrac{2 - (-8)}{-3 - 1} = -\dfrac52\\ m_{\text{altitude}} = \dfrac25\\ \dfrac{y - 3}{0 - 2} = \dfrac25\\ y - 3 = -\dfrac45\\ y = \dfrac{11}5\)

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 May 10, 2024

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