Comment on Activity 3

Since ${\displaystyle x}$ is the distance of the image of the object in the mirror from the left edge of the figure, the remaining distance to the right edge is ${\displaystyle D-x}$. Both triangles are right triangles, and the remaining distances are hypotenuses. By the Pythagorean Theorem, the distance from ${\displaystyle P}$ to ${\displaystyle R}$ is ${\displaystyle \sqrt{p^2+x^2}}$, and the distance from ${\displaystyle Q}$ to ${\displaystyle R}$ is ${\displaystyle \sqrt{q^2+\text{(}D-x{\text{)}}^2}}$. Thus, the length ${\displaystyle L\text{(}x\text{)}}$ of the toatal path is the sum of these two lengths: ${\displaystyle L\text{(}x\text{)}=\sqrt{p^2+x^2}+\sqrt{q^2+\text{(}D-x{\text{)}}^2}}$.