MathDB

There are two distinct Points

A

and

B

on a line. We color a point

P

on segment

AB

, distinct from

A,B

and midpoint of segment

AB

to red. In each move , we can reflect one of the red point wrt

A

B

and color the midpoint of the resulting point and the point we reflected from ( which is one of

A

B

) to red. For example , if we choose

P

and the reflection of

P

wrt to

A

P'

, then midpoint of

AP'

would be red. Is it possible to make the midpoint of

AB

red after a finite number of moves?

Problem Statement