There is no form of reflection that flips one point on a line and leaves the rest of the line unchanged.
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A reflection?
The line of reflection is the perpendicular bisector of any point and its image.
Draw a line joining a point and its image and find its midpoint. Repeat for another pair of point and its image. The line joining these midpoints is the line of reflection.
A reflection in a line l is a correspondence that pairs each point in the plane and not on the linewith point P' such that l is the perpendicular bisector of segment PP'. IF P is on l then P is paired with itself ... Under a reflection the image is laterally inverted. Thus reflection does NOT preserve orientation...
y=x