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The Straight Lines — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSThe Straight Lines3 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

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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