# Find a convex hull of a given set

Set $$A$$ is given as

$$A=\{(x,\frac{1}{x}) : x\geq 1\} \cup \{(0,2)\} \subset \mathbb{R^2}$$

Find a closure of a $$conv(A)$$.

I wanted to find a convex hull first but I am confused what to do with a point $$(0,2)$$.

• please provide a picture Nov 4, 2018 at 19:18

Hint: If $$B=conv(\{(x,\frac{1}{x}) : x\geq 1\})$$, then $$conv(A)$$ is the union of $$B$$ with all line segments joining $$(0,2)$$ to a point of $$B$$.