Using a white-board with graph paper or graphing technology such as geogebra be able to perform a reflection for a pre-image over the x-axis, y-axis, line y = x or line y = -x. what is the relationship to the segment formed by corresponding vertices and the line of reflection?

Explanation:

The line of reflection is the perpendicular bisector of the segment joining a point with its reflected image.

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The segment joining a point with its reflection is as short as possible consistent with the requirement that the reflected point be the same distance from the line that the original is. That means it is perpendicular to the line of reflection. Since the distance from that line is the same on either side, the line of reflection bisects the joining segment.