Question

Lines and m are perpendicular with point ofintersection P.Noah says that a 180 degree rotation, with centerhas the same effect on points in the plane asreflecting over line m. Do you agree with Noah?Explain your reasoning.

Answer 1

Consider a point Q lie on the line l.

If there is 180 degree rotation the point Q lies on the opposite of line m, which is same reflecting the point Q over the line m.

But if point Q lies on the line m, then after 180 degree rotation the point Q lies on the opposite side line l, which is not possible if point Q is reflected over line m, as after reflction of point Q over line m it must lies on same position.

So Noah is correct if point if point lies on the line l and incrrect if point lies on the line m, which means Noah is partially correct.

If point Q lies on m not on line l, then reflecting accross the line m leaves the point Q in Same place while after rotation by 180 degree with center P takes Q on other side of line