Line through the points (-2, 6) and (4, 8) is perpendicular to th… - Vidyadip

Question

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

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Answer

Slope of the line through the points (-2, 6) and (4, 8) is
$m_{1}=\frac{8-6}{4-(-2)}=\frac{2}{6}=\frac{1}{3}$
Slope of the line through the points (8, 12) and (x, 24) is
$m_{2}=\frac{24-12}{x-8}=\frac{12}{x-8}$
Since, two lines are perpendicular,
$\therefore m_1m_2$ = -1 $\Rightarrow \frac{1}{3} \times \frac{12}{x-8}=-1$
$\Rightarrow$ 4 = -(x - 8) $\Rightarrow$ x = 4

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