Interactive resource
Shortest path to a river (reflection)
Geometry. Use reflection to minimize AP + PB. Free interactive GeoGebra resource — adjust parameters in the browser.
Overview
Use reflection to minimize AP + PB.
Explanation
Classic problem: A and B on the same side of a line; find P on the line minimizing AP + PB.
Reflect A to A′, connect A′B; the intersection with the line is optimal P.
Reason: AP = A′P, so the broken path becomes a straight segment — shortest.
How to use
Drag riverside P; the dashed A′B hits the bank at the optimum.