Minimum Path Problems

1. Given a line AB with points P and Q in the same half plane determined by line AB.

Constuct a path of segments PX and XQ with X on AB such that PX + XQ is on minimal length.

Hint?

2. Given lines AB and BC perpendicular with points P and Q in the same quandrant determined by lines AB and BC.

Let X be a point on AB and Y be a point on BC. Construct the path of minimal length from segments PX, XY, and YQ.

Hint?