Question

identify which diagram represents a step in constructing a perpendicular line that is not a perpendicular bisector. (1 point)

Explanation:

Step1: Recall Perpendicular Bisector

A perpendicular bisector intersects a segment at its midpoint (\(M\) here, with \(AM = MB\)) and forms a right angle.

Step2: Analyze Non - Bisector Perpendicular

For a perpendicular line that's not a bisector, the perpendicular line should not pass through the midpoint of the segment (or the construction steps would differ, e.g., the arcs or the intersection point not being equidistant in a way that bisects the segment). The given diagram shows \(M\) as the midpoint (since \(AM = MB\)) and the perpendicular line \(CD\) through \(M\), so this is a perpendicular bisector. A diagram for a non - bisector would have the perpendicular line not passing through the midpoint of \(AB\) (e.g., the arcs drawn from a point not on the perpendicular bisector's midpoint - related setup, or the intersection point of the perpendicular not being the midpoint). But since we need to identify the diagram (assuming there are other options not shown here, but based on the concept: a step for non - bisector perpendicular would have the perpendicular line not bisecting the segment. For example, if we have a segment \(AB\) and we draw a perpendicular from a point \(P\) not on the perpendicular bisector of \(AB\), the construction steps would involve drawing arcs from \(P\) to intersect \(AB\) at two points, but those two points would not be equidistant from the midpoint of \(AB\), and the perpendicular line through \(P\) to \(AB\) would not bisect \(AB\).

Answer:

(Assuming the correct diagram is one where the perpendicular line does not pass through the midpoint of the segment. Since the given diagram is a perpendicular bisector, the correct diagram for a non - bisector perpendicular would be one with the perpendicular line not bisecting the segment, e.g., if there are options, the one where the intersection point of the perpendicular and the segment is not the midpoint, or the arcs are drawn from a point not creating equal distances on the segment. Without seeing all options, the key is that a non - bisector perpendicular construction has the perpendicular line not dividing the segment into two equal parts.)