Question

Find the distance of the point (4,2) from the line passing through the points (4,1) and (2,3).

• A. $\frac{1}{\sqrt{2}}$
• B. $-\frac{1}{\sqrt{2}}$
• C. $\frac{1}{2}$
• D. None of these

Answer 1

Answer: (A)

$\frac{1}{\sqrt{2}}$

Equation of the line passing through the point ($4,$1) and ($2,$3) is

$\frac{x-4}{y-1}=\frac{2-4}{3-1}=>\frac{x-4}{y-1}=\frac{-2}{2}=>x-4=-1(y-1)$

$=>x-4=1-y$

$=>x+y-5=0$

$\therefore$ Distance$=\frac{|4+2-5|}{\sqrt{1+1}}=\frac{|6-5|}{\sqrt{2}}=\frac{1}{\sqrt{2}}$.