# Minimizing Area

geometry

There is a rectangle and a path that goes from the bottom-left corner to the top-right. The path can only move upwards or towards the right. Draw a vertical line L through the rectangle. Now look at the area *under* the curve to the left of L, and the area *above* the curve to the right of L. Call this total area A_L. In the example figure below, L is the dotted line and A_L is the shaded area.

What is the line L that minimizes A_L?