Let A(2,4) & B(4,-2)
The slope of AB = m = \(\frac{-2-4}{4-2}= \frac{-6}{2}=-3\)
Now we know the slope of a line perpendicular is -1/m
So slope of perpendicular line to AB shall be m = \(\frac{-1}{-3}= \frac{1}{3}\)
Hence the equation of line shall be
\(y=\frac{1}{3}x+c\)
Now this line passes through (3,1)
Substituting in the equation we get
\(1= \frac{1}{3}(3)+c\)
1=1+c
c=0
Hence the equation of the line perpendicular to AB is
\(y=\frac{1}{3}x\)
