Question

Perpendicular distance of the line $AB$ from the point $(2,2)$ is

• A. $\sqrt{4}$
• B. $\sqrt{10}$
• C. $\sqrt{20}$
• D. $\sqrt{50}$

Answer 1

The correct option is C $\sqrt{20}$

Given : Point $A(0,16),B(8,0)$

$P$ is the point that passes through A and B

Perpendicular distance of the line AB from point $(2,2)$

Equation of line AB $=y-0=\frac{0-16}{8-0}(x-8)$

$8y=-16x+12816x+8y=128$

Equation of AB $=2x+y=16$

$2x+y-16=0$

Perpendicular distance $=\left|\frac{{ax}_1+{by}_2+C}{\sqrt{a^2+b^2}}\right|\left\{\right(x,y)=(2,2\left)\right\}$

$=\left|\frac{2\left(2\right)+1\left(2\right)-16}{\sqrt{{\left(2\right)}^2+{\left(1\right)}^2}}\right|=\left|\frac{-10}{\sqrt{5}}\right|=2\sqrt{5}=\sqrt{20}$

Therefore perpendicular distance is equal to $\sqrt{20}$ Units.