Im trying to find 2x2 matrices that when you multiply the line segment by the matrix you get a symmetry of the initial line segment. I know that the identity matrix will give you the identity symmetry, but I know there are 3 other symmetries in R2 so I am not sure what else those are.
2026-03-31 23:28:20.1774999700
Linear transformation that finds symmetry of a line segment?
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Reflection by bisecting perpendicular line. （aka perpendicular bisector?)
Reflection by the line
Rotation of 180 degrees about the mid-point.
Btw, per explanation of the symmetry-group tag, what you are seeking is not standard definition of symmetry groups. Though we can easily see the answer without formal definitions, if you want more details, you should define what you mean by symmetry groups.