Heron's Principle of Reflection/Examples/Journey to the River

Example of Use of Heron's Principle of Reflection
Mary, who is standing at a point $S$, wants to walk to the point $T$.


 * Herons-Reflection-Principle-River.png

However, first she wants to take a drink of water from a river.

She wants to walk as short a distance as possible.

To what point on the riverbank should she walk?

Solution
Imagine the point $T'$ which is $T$ reflected in the line taken by the river bank.

The point $P$ is that point on the river bank directly in line with $S$ and $T'$.


 * Herons-Reflection-Principle-River-Solution.png

Or you can reflect $S$ in the line taken by the river bank to get point $S'$.

Then $P$ is the point on the river bank directly in line with $S'$ and $T$.