The slope of two perpendicular lines m1 and m2 are related as m1* m2 = -1.
The slope of the line through (1,3) and ( 2,6) is :
m = (6 - 3)/(2 - 1)
=> m = 3
A line perpendicular to this line has a slope -1/3.
The slope of the required line is -1/3.
We know that 2 line are perpendicular if and only if the product of the values of their slopes is -1.
We can find the slope of the line that passes through the given points.
m1 = (y2 - y1)/(x2 - x1)
m1 = (6-3)/(2-1)
m1 = 3/1
m1 = 3
The product of the slopes is:
m1*m2 = -1
-3*m2 = -1
We'll divide by -3:
m2 = 1/3
The slope of the perpendicular line to the line that passes through the points (1,3) and (2,6) is m2 = 1/3.