1. The problem is to understand the concept of rotation in geometry. 2. Rotation is a transformation that turns a figure about a fixed point called the center of rotation. 3. The amount of turn is specified by the angle of rotation, usually measured in degrees. 4. The direction of rotation can be clockwise or counterclockwise. 5. The formula for rotating a point $(x,y)$ about the origin by an angle $\theta$ counterclockwise is: $$x' = x\cos\theta - y\sin\theta$$ $$y' = x\sin\theta + y\cos\theta$$ 6. This formula comes from trigonometric relationships in the coordinate plane. 7. To rotate a point, substitute the coordinates and the angle into the formulas and simplify. 8. For example, rotating point $(1,0)$ by $90^\circ$ counterclockwise: $$x' = 1\cdot\cos 90^\circ - 0\cdot\sin 90^\circ = 0$$ $$y' = 1\cdot\sin 90^\circ + 0\cdot\cos 90^\circ = 1$$ 9. So the point $(1,0)$ becomes $(0,1)$ after a $90^\circ$ rotation. 10. This method applies to any point and any angle of rotation about the origin.