You would find stars that are cool and dim in the lower right corner of the Hertzsprung-Russell (H-R) diagram.

Here's why:

* Cool: The H-R diagram's horizontal axis represents temperature. Cooler stars are located on the right side of the diagram.

* Dim: The H-R diagram's vertical axis represents luminosity (brightness). Dim stars are located at the bottom of the diagram.

Therefore, the intersection of these two areas, the lower right corner, contains stars that are both cool and dim. This region is typically occupied by red dwarf stars, which are the most common type of star in the Milky Way.