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

\frac{\sqrt{17}}{2}

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\sqrt{\frac{17}{2}}

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\sqrt{\frac{17}{14}}

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\frac{17}{2}

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Solution

The correct option is D $\sqrt{\frac{17}{2}}$
$m_{1} = \frac{0 - 3}{5 - 0} = - \frac{3}{5} (y - 3) = - \frac{3}{5} (x - 0) 5 y - 15 = - 3 x 3 x + 5 y - 15 = 0 5 y - 15 = - 3 x 3 x + 5 y - 15 = 0$
Length of perpendicular from $(4, 4)$
$= \frac{3.4 + 5.4 - 15}{\sqrt{25 + 9}} = \frac{17}{\sqrt{34}}$

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