So, the point given is A = ( 4, 2 ) and the line given is

p: (x,y) = (1,2) + s[-1 3]

Okay.. so I re-write the line in form ax + by = c which would be..

y - 2 = (-1/3)(x-1)

y = (-1/3)x + (7/3)

(1/3)x - y = (7/3)

so a = (1/3) b = (-1)

so a normal to the line p would be n = [1/3 -1]

I find a point on line p, I pick Q = (1,2)

I find a new vector by subtracting Q from A.. so (4,2) - (1,2) would be the new vector r.

now for me to find the distance of the point, I project n (r).. so

I take a unit vector of n and take the dot product of it with r and to find the scalar. then I take the scalar and multiple it by n again.

then i find the distance of the new vector and that is the distance of the point?

Does that make sense, or am I completely wrong?