I'm having trouble with this question:

Show that the midpoint bteween any two feasible points in a convex program is itself feasible.

I can show that any point on a line drawn between any two feasible points in a convex program is itself feasible.

If the points are and , then any point on the line between then can be

expressed as for some .

Say is convex,

Since and both and are feasible. Furthermore, since is affine,

Therefore any point on the line is feasible between any two feasible points in a convex program.

The question is, how do I show that the midpoint between any two feasible points in a convex program is also feasible??

Thanks for your help!