Question

What is the best next step in the construction of the perpendicular bisector of AB?

A.Use a compass to draw a circle centered at B with a radius that is ½ the length of AB.

B.Use a straightedge to draw a quadrilateral with vertices at A, B, and each of the points where the two circles intersect.

C.Use a compass to draw a circle centered at A with a radius that is ½ the length of AB.

D.Use a straightedge to draw a line segment from one of the points where the two circles intersect to the other point where the two circles intersect.

Answer 1

Option D is the next step in the construction of the perpendicular bisector of AB. Here's the explanation:

D. Use a straightedge to draw a line segment from one of the points where the two circles intersect to the other point where the two circles intersect.

The construction steps

Start with line segment AB.

Use a compass to draw a circle centered at B with a radius equal to half the length of AB.

This circle will intersect AB at two points. Connect these two points with a straightedge to form the perpendicular bisector of AB.

Therefore, the correct next step is to use a straightedge to draw a line segment from one of the points where the two circles intersect to the other point where the two circles intersect (option D).

This new line drawn will intersect line AB at the midpoint of the line

Answer 2

This construction shows how to draw the perpendicular bisector of a given line segment with compass and straightedge or ruler. This both bisects the segment (divides it into two equal parts, and is perpendicular to it. It finds the midpoint of the given line segment.