MathDB

On a board are drawn the points

A,B,C,D

. Yetti constructs the points

A^\prime,B^\prime,C^\prime,D^\prime

in the following way:

A^\prime

is the symmetric of

A

with respect to

B

B^\prime

is the symmetric of

B

wrt

C

C^\prime

is the symmetric of

C

wrt

D

and

D^\prime

is the symmetric of

D

wrt

A

. Suppose that Armpist erases the points

A,B,C,D

. Can Yetti rebuild them?

\star \, \, \star \, \, \star

Note. Any similarity to real persons is purely accidental.

Problem Statement