How do the coordinates change when you rotate a shape?

When you rotate a shape around a point (typically the origin), the coordinates of each point change based on the angle of rotation. For a rotation by an angle θ counterclockwise, the new coordinates (x', y') of a point (x, y) can be calculated using the formulas: x' = x * cos(θ) - y * sin(θ) and y' = x * sin(θ) + y * cos(θ). The rotation transforms the position of the points while maintaining the shape's dimensions and angles.