problem: How many units long is a segment whose endpoints are $(-4,1)$ and $(1,13)$?
solution: We use the distance formula: $\sqrt{(-4 - 1)^2 + (1 - 13)^2},$ which is $\sqrt{25 + 144} = \sqrt{169} = \boxed{13}$.
  
  - OR -
  
  We note that the points $(-4,1)$, $(1,13)$, and $(1,1)$ form a right triangle with legs of length 5 and 12. $(5,12,13)$ is a Pythagorean triple, so the hypotenuse has length $\boxed{13}$.