Final answer:
Stars that burn helium at their cores on the Hertzsprung-Russell diagram are found to the left of and somewhat below their former position as red giants, indicating higher temperatures and generally lower luminosities.
Step-by-step explanation:
On a Hertzsprung-Russell diagram, stars that are burning helium at their cores are found to the left of and somewhat below their position as red giants. After a star like our Sun uses up its hydrogen and undergoes the helium flash, it finds balance again in fusing helium into heavier elements like carbon and sometimes oxygen. This stage of its life is represented on the H-R diagram by a shift to higher temperatures and generally lower luminosities, positioning such stars along a path known as the horizontal branch (for stars like the Sun) or sometimes in a region called the asymptotic giant branch (for more massive stars).