There are several ways that you can attack this problem. I'm going to use a parameterized approach similar to the one used for Problem 29. *Line-line intersection*.

Suppose the point is (*px, py*) and the line is given by *p0 + t × v*. Then the distance between the point and a point on the line is given by the following:

We need to find the value of *t* that minimizes this equation. You can do that with one trick and a little calculus.

The trick is to note that the minimum of this equation has the same *X* coordinate that minimizes the equation squared. The following shows the squared equation:

Here comes the calculus. To minimize ...