Question

Consider the incomplete paragraph proof.

Given: P is a point on the perpendicular bisector, l, of MN.
Prove: PM = PN

Line l is a perpendicular bisector of line segment M N. It intersects line segment M N at point Q. Line l also contains point P.

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

Answer 1

point M

Reason: reflecting across the perpendicular bisector l fixes P (since P lies on l) and sends M to N, and reflections preserve distances, so PM = PN.