How do we know that there are red giants and supergiants on the hr diagram?

When stars have exhausted all their hydrogen fuel, they evolve to red giants. Their outer layers of gas expand and cool; therefore, the stars move to the right on the H-R diagram. Although a star cools when it becomes a red giant, it grows so large its luminosity (or total power emitted) increases. On the H–R diagram, the star therefore leaves the main-sequence band and moves upward (brighter) and to the right (cooler surface temperature). Over time, massive stars become red supergiants, and lower-mass stars like the Sun become red giants.

personal, she chose to do it.