Question

A straight line passes through the point $(5,0)$ and $(0,3)$. The length of the perpendicular from the point $(4,4)$ on the line is

• A. $\frac{17}{\sqrt{34}}$
• B. $\sqrt{\frac{17}{2}}$
• C. $\frac{15}{\sqrt{34}}$
• D. $\frac{17}{5}$

Answer 1

The correct option is A $\frac{17}{\sqrt{34}}$

Equation of line passing through $(5,0)$ and $(0,3)$ is given by,

$y-0=\frac{3-0}{0-5}(x-5)$, use two point form of line

$\Rightarrow y=\frac{3}{-5}(x-5)$

$\Rightarrow -5y=3(x-5)$

$\Rightarrow 3x+5y-15=0$

Therefore distance of this line line from the point $(4,4)$ is

$=\frac{\left|3\right(4)+5(4)-15|}{\sqrt{3^2+5^2}}=\frac{17}{\sqrt{34}}$