Isometry

Say to the believing men: Let their gaze, and maintains his cock; such is purer for them, surely Allah is Aware of what they do. (An-Nur: 30)

 
Isometry is a transformation of Reflection (reflection), translations (shift), and Rotation (rotation) on a line that maintains the distance (the length of a segment)

S reflection is Ms function by definition fo every point of P at plane as follow :

1  If P member of S then Ms (P) = P

2  if P isn’t member of S then Ms (P)  = P’ such that S as bisector that perpendicular from PP’

Ms (P) = P

M :  reflection functions

S : mirror

(P) = Object

P = Shadow

1                      1 Reflection is transformation

2  Reflection line properties is preserved to distance. It’s mean A’B’ = AB

3  Transformation as preservd to distance that can called as Isometry

4  Reflection is isometry