Example of Pointed Cone

Question

A Cone $K$ is pointed if $k \in K$ and $-k \in K$ then $K=0$.

but

in this example how to check this is pointed or not.

$ K = \{ (x,y) \in R^2 : \left|x\right|\leq \left|y\right| \} $

Answer 1

Take $(x,y) = (3,4)$ and $(x,y) = (-3,-4)$. Both these points satisfy $|x| \le |y|$ but $(3,4) \ne (0,0)$. Hence the cone is not pointed.