What's the Shortest Distance from a Point to a Line?

The shortest distance from a point to a line is the segment perpendicular to the line from the point. Let's think about why.

What would happen if this line wasn't perpendicular?

So say that we draw a segment from the point (Let's call this point A)to the line, that is not perpendicular to it.Let this segment intersect the line at point B. Now draw the segment perpendicular to the line from point A let this intersect at point C.

Now we see that $AC^2+BC^2=AB^2$. So quite obviously $AC<AB$, and therefore the segment perpendicular to the line from a point is the shortest.