How far in arc seconds is a planet from its star? The star is 12 parsecs away from earth. The planet is 1 AU from its star
Because a separation of 1 au subtends an angle of 1 arcsecond at 1 parsec. That is the definition of a parsec. As you move further away, the angle gets smaller by a factor of the increase in distance. 

Just draw a right-angled triangle where the base length is the distance and the height is the star-planet separation. Now increase the base length and ask yourself what happens to the angle subtended at the Earth? NB All angles are small so $\theta \simeq \tan \theta$.