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Straight Lines — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsStraight Lines2 Marks
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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