Not a question, but I want to see if people know how to solve this. This problem is one of my favorite problems!

Let X,Y, and Z be points such that $\frac{XZ}{XY} = \frac{ZY}{XY} = \frac{1}{2}.$If $Y = (1, 7)$, $Z = (-1, -7)$, then what is the sum of the coordinates of X?