Question

step 3: construct an angle and a perpendicular bisector.
a) the construction of creating the perpendicular bisector of is started below. how would the construction be different if you changed the compass setting in the next step of the perpendicular bisector construction?

Explanation:

Step1: Recall perpendicular - bisector construction

In the standard construction of a perpendicular bisector of a line segment PQ, we first set the compass width to more than half the length of PQ. We draw arcs from both endpoints P and Q.

Step2: Analyze effect of compass - setting change

If the compass setting is increased in the next step: The arcs drawn from the endpoints of the line - segment will have a larger radius. The intersection points of these arcs (which are used to draw the perpendicular bisector) will be farther away from the line segment PQ. If the compass setting is decreased: The arcs will have a smaller radius. If the new radius is less than half the length of the line segment PQ, the arcs from the two endpoints will not intersect, and we will not be able to construct the perpendicular bisector.

Answer:

If the compass setting is increased, the intersection points of the arcs used to construct the perpendicular bisector will be farther from the line segment. If the compass setting is decreased to less than half the length of the line segment, the arcs will not intersect and the perpendicular bisector cannot be constructed.