Final answer:
Allie is using geometric construction to find the perpendicular bisector of a line segment, which is a key concept in geometry used for dividing a segment into two equal parts and finding points that are equidistant from the segment's endpoints.
Step-by-step explanation:
Allie is finding a point on a line segment using a geometric construction. The steps described involve creating arcs using a compass from both ends of the line segment and connecting the intersections of those arcs with a straight line. The point where this new line intersects the original line segment is the perpendicular bisector of the segment.
This point has special properties; it is equidistant from the endpoints of the segment and divides the segment into two equal parts. When constructing the perpendicular bisector using these steps, we use the properties of circles and segments to ensure the point is accurately determined. This construction is a fundamental concept in geometry, which helps in various analytical techniques, such as finding the midpoint of a segment or solving problems involving distances and angles.