The line passing through the points (-2, 6) a | vedclass

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(A) Let the slope of the first line be $m_{1}$ and the slope of the second line be $m_{2}$.The slope of the line through $(-2, 6)$ and $(4, 8)$ is:$m_

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$4$

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(A) Let the slope of the first line be $m_{1}$ and the slope of the second line be $m_{2}$.The slope of the line through $(-2, 6)$ and $(4, 8)$ is:$m_{1} = \frac{8 - 6}{4 - (-2)} = \frac{2}{6} = \frac{1}{3}$.The slope of the line through $(8, 12)$ and $(x, 24)$ is:$m_{2} = \frac{24 - 12}{x - 8} = \frac{12}{x - 8}$.Since the two lines are perpendicular,the product of their slopes must be $-1$:$m_{1} 	imes m_{2} = -1$.Substituting the values:$\frac{1}{3} 	imes \frac{12}{x - 8} = -1$.Simplify the equation:$\frac{4}{x - 8} = -1$.Multiply both sides by $(x - 8)$:$4 = -(x - 8)$.$4 = -x + 8$.$x = 8 - 4$.$x = 4$.

The line passing through the points $(-2, 6)$ and $(4, 8)$ is perpendicular to the line passing through the points $(8, 12)$ and $(x, 24)$. Find the value of $x$.

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