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**We have a vector p = (0, 0, 2) in R^3 and we have the subset S = {xp where x >= 0} + T, where T is the convex hull of 5 vectors: (2,2,2), (4,2,2), (2,4,2), (4,4,6) and (2,2,10).**

How do I show that the subset T is a closed and convex subset?

I know that a subset is called convex if it contains the line segment between any two of its points: (1-t)u + tv for every u and v in the subset. I've tried to take two of those 5 vectors and see if there contains a line segment, but so far, it doesn't make any sense. I hope that you can help me with this problem.