There are two towns near a shore, and one town is slightly closer to the shore than the other town. They want to build a pier on the shoreline, as well as a path from the pier to each town. They want to use as little material as possible, so they need to put the pier in a location on the shoreline that minimizes the total length of both paths added together. Where on the shoreline should they build the pier?

Here's the Answer

To find the answer, first draw a horizontal line to represent the shoreline, then a dot below that line on the right and the left for where each town is located (one will be further below the line than the other).
Next, fold the paper along the shoreline, and mark the location of the town closest to the shore so it bleeds through the paper. Unfold your paper and you'll see the shoreside town's "reflected" location. Take a ruler and draw a straight line from the further town to that reflected location, and note where on the shoreline it hits. That is where you should build your pier. You can try any other location, and you won't find one any closer to both towns.
Did you get it? Watch the video above for a deep dive into why this works.