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