Find the point on the line $y = x + 2$ that is nearest to the point $(1,1)$. The shortest distance from point to point.
I honestly don't even know where to begin with this one.
Hint: If you want to use calculus, let $x$ be the horizontal coordinate of the point on the line. Then the point is $(x,x+2)$. You can calculate the distance from this to $(1,1)$ as a function of $x$, set the derivative to $0$.
Alternately, the shortest distance is along a perpendicular. Do you know the relation between the slope of a line and the slope of the perpendicular? Make a line through $(1,1)$ with that slope and find the intersection with your line.