is a positive ray is a convex cone?

Question

A definition of a convex cone is given here, could anyone tell me whether a ray $C=\{(x,y): y=mx, x\ge 0,y \ge 0, m=\tan \theta, 0< \theta< 90\}$ on the positive quadrant satisfies the condition $4$? I can see 1,2,3, are satisfied. Thanks!