Answer:
1. B) Parallax
3. D) Apparent brightness and distance to the star
4. A) Red giant
5. B) Blue
Explanation:
1. In order to measure the distance to a nearby star, astronomers use parallax method. In this method, parallax angle is measured. The star appears to move against a fixed background when viewed from two different position of Earth in its orbit.

where, <em>d</em> is the distance in parsecs and <em>p</em> is the parallax angle in arc-second.
2. Luminosity of a star is the energy emitted by a star's surface. It measured in watts. In order to measure the luminosity of a star, apparent brightness (b) and distance to the star (d) is required. Following formula can be used to measure the luminosity of a star:

3. The H-R diagram is the plot of stars based on their luminosity, color and temperature. In the upper right of the H-R diagram, red giants are located. These are the cool and bright stars. An average mass star like the sun expands and becomes a red giant when it runs off its fuel before ending up as a white dwarf.
4. Color of a star indicated its surface temperature. A star emits different wavelengths but a peak wavelength can be observed from its spectrum which indicates the star's effective temperature. So, cool stars are red in color where as hot and bright stars are blue in color.