I'm actually a little ashamed to ask this,
Suppose A and B are not 0. Consider a line "l" whose cartesian equation is $Ax+ By + D = 0$. Suppose that $P_0 = (x_0,y_0)$ does not lie on "l". Show that $n = (A,B)$ is a vector that is perpendicular to "l"
I am trying to do this without the dot-product which makes it even more embarassing. So I know that in order for two lines to be consider perpendicular that either their slopes have to be negative reciprocals of each other or in dot-product form that they equal 0. How can I use that point and the normal "n" to show the vector is perpendicular?