Need help with vector equation question

Consider the vector equation x = p + t (q - p), where p and q correspond to distinct points P and Q in 2D or 3D.

1. Show that this equation describes the line segment PQ as t various from 0 to 1.

2. For which value of t is x the midpoint of PQ, and what is x in this case?

Thanks for any help.

1; x = [ 1 - t ] p + t q , when t = 0 , x = p and t = 1 , x = q

2; and when t = 1 / 2 , x = [p+q] / 2