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?

GSP file?    Click HERE.

 

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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.

 

 

The desired result is shown at the right.

 

Hint?

 

GSP file?    Click HERE.