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A straight line passes through the points $(5,0)$ and $(0,3)$. The length of the perpendicular from the point $(4,4)$ on the line is
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Verified Answer
The correct answer is:
$\sqrt{\frac{17}{2}}$
Suppose equation of line is
$\frac{x}{5}+\frac{y}{3}=1$
$\Rightarrow \quad 3 x+5 y-15=0$
Now, length of perpendicular from $(4,4)$ on $3 \mathrm{x}+5 \mathrm{y}-15$ $=0$ is
$P=\left|\frac{3.4+5.4-15}{\sqrt{34}}\right|=\left|\frac{17}{\sqrt{34}}\right|=\frac{\sqrt{17} \cdot \sqrt{17}}{\sqrt{17} \cdot \sqrt{2}}$
$P=\sqrt{\frac{17}{2}}$
$\frac{x}{5}+\frac{y}{3}=1$
$\Rightarrow \quad 3 x+5 y-15=0$
Now, length of perpendicular from $(4,4)$ on $3 \mathrm{x}+5 \mathrm{y}-15$ $=0$ is
$P=\left|\frac{3.4+5.4-15}{\sqrt{34}}\right|=\left|\frac{17}{\sqrt{34}}\right|=\frac{\sqrt{17} \cdot \sqrt{17}}{\sqrt{17} \cdot \sqrt{2}}$
$P=\sqrt{\frac{17}{2}}$
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