As they age, ___________ stars move up and to the right on an H-R diagram.

The Hertzsprung-Russell diagram or H-R diagram is a plot between the temperature of a star and its luminosity. It can also be drawn between the color of the star and the absolute magnitude. Either way, this plot is extremely useful to astronomers. Any given star can be plotted on this diagram and the position of the star gives an idea of the life stage the star is in. For example, the main-stage stars (such as our sun) occupy the central diagonal region of the diagram, from the upper left to the bottom right. White dwarfs are in the bottom left corner, while red giants occupy the top right area in the diagram.

When stars are in the main sequence, they are converting hydrogen to helium and using this nuclear reaction to produce energy. When all the hydrogen in a star's core runs out, stars convert into red giants. A red giant has higher luminosity than a main-sequence star and hence is found on the upper side of the diagram. Red giants also have a higher radius and lower temperature than the main-sequence stars and hence move to the right of the main sequence stars. 

Thus, as stars age, main sequence stars convert into red giants and move up and to the right on the H-R diagram. 

Hope this helps.