Find a convex hull of a given set

Question

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 $(0,2)$.

Answer 1

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 $B$.