Consider the incomplete paragraph proof. Given: P is a point on the perpendicular bisector, I, of overline (MN). Prove: PM=PN Because of the unique line postulate, we can draw unique line segment PM Using the definition of reflection. overline (PM) can be reflected over line 1. By the definition of reflection, point P is the image of itself and point N is the image of __ Because reflections preserve length, PM=PN. point M point Q segment PM segment QM

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Consider the incomplete paragraph proof. Given: P is a point on the perpendicular bisector, I, of overline (MN). Prove: PM=PN Because of the unique line postulate, we can draw unique line segment PM Using the definition of reflection. overline (PM) can be reflected over line 1. By the definition of reflection, point P is the image of itself and point N is the image of __ Because reflections preserve length, PM=PN. point M point Q segment PM segment QM

Answer 1

This is a geometry problem that involves the properties of a perpendicular bisector. The question is asking to fill in the blank in a proof that demonstrates that a point on the perpendicular bisector of a line segment is equidistant from the endpoints of the segment. In the proof, a line segment PM is drawn from point P to one endpoint of the line segment, point M. Then, PM is reflected over the perpendicular bisector. By the definition of reflection, point P is the image of itself and point N is the image of the point that is reflected. In this case, the point that is reflected to become point N is point M, because M is the other endpoint of the line segment. Therefore, the correct answer is "point M".

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