Question

consider the incomplete paragraph proof.
given: p is a point on the perpendicular bisector, l, of mn.
prove: pm = pn
because of the unique line postulate, we can draw unique line segment pm. using the definition of reflection, pm can be reflected over line l. 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

Explanation:

When reflecting a point over a line, if the line is the perpendicular bisector of a segment, the endpoints of the segment are reflections of each other. Here, since \(l\) is the perpendicular bisector of \(\overline{MN}\), reflecting \(\overline{PM}\) over \(l\) (with \(P\) being on \(l\) so it maps to itself) means \(M\) maps to \(N\) (because reflections over the perpendicular bisector of a segment swap the endpoints of the segment).

Answer:

A. point M