11. Point-line distance

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 ...

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