## Find the distances of the point using vectors

Okay, I am given a point.. A= (4,2) and I am supposed to find its distance to several lines.

l: y = 3x - 10 and k: y = (2/3)x - 20/3

So, I thought.. use vectors! Since, a point + a vector = another point, right? So, wouldn't the distance between that new point and A be the distance to the line itself?

Kind of makes sense to me.. Except when I go and try to do it.. I'll use l for an example..

(4,2) + [1,3] = (5,5)... sqrt{(5-4)^2 + (5-2)^2} sqrt(1 + 9)...so the distance between A and (5,5) is sqrt(10)

But... the point A = (4,2) is in fact on the line l itself. y = 3(4) - 10 is equal to 2..

So wouldn't the distance be zero?

Help ; (