Question

question 2 of 10

if \\(a\\) and \\(b\\) are two points in the plane, the perpendicular bisector of \\(\overline{ab}\\) is the set of all points equidistant from \\(a\\) and \\(b\\).

a. true
b. false

Explanation:

Analyze the geometric definition

The statement describes the perpendicular bisector of a line segment \(\overline{AB}\) in a plane. By definition, the perpendicular bisector of a segment is the line perpendicular to the segment at its midpoint.

Evaluate the locus property

A fundamental theorem in geometry states that a point is on the perpendicular bisector of a segment if and only if it is equidistant from the endpoints of the segment. Therefore, the perpendicular bisector of \(\overline{AB}\) is indeed the set of all points in the plane equidistant from \(A\) and \(B\).

Determine the truth value

Since the statement matches the standard geometric definition and locus property of a perpendicular bisector, the statement is true.

Answer:

• A. True (Correct answer)
• B. False