Slopes of Perpendicular Lines

You may recall this from past math classes:

If two lines are perpendicular, then the product of their slopes is -1.

This is another way to look at what goes on when you make a normal vector to a given 2D vector by swapping elements and negating one:

If  v   =   ( x, y )^T

Then  v'   =  ( -y, x )^T   is orthogonal,

because   ( x, y)^T · ( -y, x )   is -xy + yx   =   0.

The slope of   ( x, y )^T   is y/x.

The slope of   ( -y, x )^T   is -x/y.

The product of the slopes is   y/x * -x/y   =   -(xy)/(xy)   =   -1