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What angle does the line segment joining $(5,2)$ and $(6,-15)$ subtend at $(0,0) ?
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Verified Answer
The correct answer is:
$\frac{\pi}{2}$
Slope of line joining $(5,2)$ and $(0,0)$
$\tan \mathrm{A}=\mathrm{m}_{1}=\frac{2-0}{5-0}=\frac{2}{5}$
Slope of line joining $(6,-15)$ and $(0,0)$
$\tan \mathrm{B}=\mathrm{m}_{2}=\frac{-15}{6}=\frac{-5}{2}$
Now, $\mathrm{m}_{1} \cdot \mathrm{m}_{2}=\frac{2}{5}\left(-\frac{5}{2}\right)=-1$
Hence, both lines are perpendicular. and than angle
between them $=\frac{\pi}{2}$
$\tan \mathrm{A}=\mathrm{m}_{1}=\frac{2-0}{5-0}=\frac{2}{5}$
Slope of line joining $(6,-15)$ and $(0,0)$
$\tan \mathrm{B}=\mathrm{m}_{2}=\frac{-15}{6}=\frac{-5}{2}$
Now, $\mathrm{m}_{1} \cdot \mathrm{m}_{2}=\frac{2}{5}\left(-\frac{5}{2}\right)=-1$
Hence, both lines are perpendicular. and than angle
between them $=\frac{\pi}{2}$
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