Chapter 13.1, Problem 5MC

When a line is rotated about a point O, by angle $\alpha$, the image of the line can be found by rotating any two points on the line. A different way is to drop the perpendicular from O to l. If P is the point where the perpendicular intersects l, we find P′ the image of P under rotation by $\alpha$ about O and construct k the perpendicular line to $\overline{OP\prime }$ at P′. Explain why k is the image of l.