# Assignment 2

Supplementary image to Q1.

# Fat Points

Proof by contradiction. Assume that the line segment between points $$P,Q$$ has maximum pairwise distance, and that $$Q$$ does not lie on a vertex. Let the point on the boundary of our hull found by extending the line $$PQ$$ be denoted $$Q'$$. This boundary segment is defined between two vertices on our convex hull which we refer to as $$A$$ and $$B$$. See $$\mathbf{Fig. 1}$$ for clarification.

## Q Lies on the Interior of the Hull

Clearly $$|PQ'|>|PQ|$$. In the following section we show that there is always a line-segment longer than $$|PQ'|$$. By the transitive property of inequality this segment must also be longer than $$PQ$$, a contradiction.