Question

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

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

Answer 1

Answer: (B)

The equation of line passing through points $(5,0)$ and $(0,3)$ is
$(y-0)=\frac{(3-0)}{0-5}(x-5)$
$\Rightarrow y=\frac{3}{-5}(x-5)$
$\Rightarrow -5y=3x-15$
$\Rightarrow 3x+5y-15-0$
$\therefore$ The length of perpendicular from the point $(4,4)$ to the above line is
$d=\frac{(3\times 4+5\times 4-15)}{\sqrt{3^2+5^2}}$
$\equiv \frac{12+20-15}{\sqrt{9+25}}$
$=\frac{17}{\sqrt{34}}=\sqrt{\frac{17}{2}}$