Question

multiple choice 2 points segment xy has midpoint m. a perpendicular bisector of xy is constructed. which statement about the perpendicular bisector is always true? it passes through point m. it passes through point x. it makes a 45 - degree angle with xy. it makes a 30 - degree angle with xy.

Explanation:

Step1: Recall definition of perpendicular bisector

A perpendicular bisector of a line - segment is a line that is perpendicular to the segment and passes through its mid - point.

Step2: Analyze each option

Given segment $XY$ with mid - point $M$, by the definition of a perpendicular bisector, it must pass through $M$. It does not necessarily pass through $X$. A perpendicular bisector makes a 90 - degree angle with the line - segment it bisects, not 45 degrees, 30 degrees.

Answer:

It passes through point M.