Question

logical reasoning tell whether the information in the diagram allows you to conclude that c is on the perpendicular bisector of ab. explain your reasoning. 10.

Explanation:

Step1: Recall the definition of perpendicular bisector

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

Step2: Analyze the given diagram

In the diagram, \(P\) is the mid - point of \(\overline{AB}\) (indicated by the equal marks on \(AP\) and \(PB\)) and the line \(CP\) is perpendicular to \(\overline{AB}\) (indicated by the right - angle symbol).

Step3: Apply the property of points on a perpendicular bisector

By the property that any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. Since \(CP\) is the perpendicular bisector of \(\overline{AB}\), and \(C\) lies on \(CP\), we can conclude that \(C\) is on the perpendicular bisector of \(\overline{AB}\).

Answer:

Yes, \(C\) is on the perpendicular bisector of \(\overline{AB}\). The diagram shows that the line through \(C\) and \(P\) is perpendicular to \(\overline{AB}\) and \(P\) is the mid - point of \(\overline{AB}\), so by the definition of a perpendicular bisector, \(C\) lies on the perpendicular bisector of \(\overline{AB}\).