Stars that are cool and dim on the Main Sequence are located at the lower right end of the Hertzsprung-Russell (H-R) diagram.

Here's why:

* Temperature: The H-R diagram plots stars based on their temperature (hotter to cooler going from left to right). Cool stars reside on the right side.

* Luminosity: The H-R diagram also plots stars based on their luminosity (brighter to dimmer going from top to bottom). Dim stars reside on the bottom of the diagram.

Therefore, cool and dim stars are found where these two axes intersect - the lower right corner of the Main Sequence.

Examples of such stars include red dwarfs.