Optimization problem

Question

A farmer's house sits 2 miles due south of a river. The diagram below shows the path that the farmer takes from his house to the river every day in order to bring water to a farm located 6 miles south from the river and 2 miles east of the farmer's house. By choosing a different point P on the river to draw water, the farmer is able to walk different distances to do this task. Find the minimum distance possible that the farmer has to walk.

Enter an exact answer or round to the nearest hundredth of a mile.

Answer 1

The point P is 1 mile East of the house on the river.

Can you determine the distance and answer?