Question

When would the vertex of an angle have the same coordinates after a rotation?

Answer 1

To have the same coordinates after a rotation, the degrees of the rotation would be 360.

Explanation:

When a point (x,y) is rotated about the origin (0,0) counterclockwise by an angle θ, the coordinates of the new point (x′,y′) are :

x′=xcos(θ)−ysin(θ),

y’=xsin(θ)+ycos(θ).

To have the same coordinates after a rotation, the degrees of the rotation would be 360.