Question

Sasha is bisecting a segment. First, she places the compass on one endpoint, opens it to a width larger than half of the segment, and swings an arc on either side of the segment. Then, she keeps the compass the same width and places it on the other endpoint. What is her next step?

Options:

Option 1: Swing arcs on both sides to intersect the first two arcs created.
Option 2: Swing an arc that intersects the segment.
Option 3: Swing arcs that intersect a point that is not on the segment.
Option 4: Swing an arc that intersects the opposite endpoint.

Answer 1

The correct next step in bisecting a segment with a compass is to swing arcs from both endpoints to intersect the first arcs creates, forming a line segment that bisects the original at the midpoint.

Step-by-step explanation:

Sasha is in the process of bisecting a segment using a compass, which is a common geometric construction technique. After swinging arcs from both endpoints of the segment with the compass set to a width larger than half of the segment, her next step should be Option 1: Swing arcs on both sides to intersect the first two arcs created. These intersection points will then form a line segment perpendicular to the original segment, crossing it at the midpoint and thus bisecting the original segment accordingly.