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

To complete the paragraph proof, the correct answer is:

**point M**

Here's the reasoning:

When we reflect point M over line l (the perpendicular bisector), the image of point M after reflection will be point N. Thus, the correct completion of the statement, which denotes the relationship in the reflection, would be that point N is the image of point M under that reflection. Therefore, we can conclude that PM = PN because reflections preserve length.