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

The slope of the line joining (-2, 6) and (4, 8) is
$\text{m}_1=\frac{8-6}{4-(-2)}=\frac{2}{6}=\frac{1}{3}$
The slope of the line joining (8, 12) and (x, 24) is
$\text{m}_2=\frac{24-12}{\text{x}-8}=\frac{12}{\text{x}-8}$
Since the lines are perpendikular two each other
$\text{m}_1\times\text{m}_2=-1$
$\frac{1}{3}\times\frac{12}{\text{x}-8}=-1$
$\Rightarrow4=8-\text{x}$
$\Rightarrow\text{x}=4$

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