Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. in the given diagram, two sets of arcs are drawn above and below segment ab using a compass set to the same width. for one set of arcs, the compass needle is positioned at point a. for the second set of arcs, the compass needle is positioned at point b. a line drawn through the intersections of these two sets of arcs determines the location of point c. based on this construction, cb = units and ab = units

Explanation:

Step1: Identify the construction

This is the construction of the perpendicular - bisector of a line segment. A line drawn through the intersections of the two sets of arcs is the perpendicular - bisector of segment AB, which divides AB into two equal parts.

Step2: Determine the length of CB

Since C is the mid - point of AB and AC = 16 units, then CB=AC. So, CB = 16 units.

Step3: Calculate the length of AB

Since AB=AC + CB and AC = CB = 16 units, then AB=16+16 = 32 units.

Answer:

CB = 16, AB = 32