Question

select the correct answer.
based on the construction shown, what is the next step when bisecting line segment ab using string?
a. set the string length between point a and where the arc crosses segment ab.
b. set the string length at point a and at the top of the arc.
c. using a straightedge, draw a line perpendicular to segment ab so it crosses the arc in two places.
d. keep the string length and draw an arc centered at point b that crosses the other arc in two places.

Explanation:

Step1: Recall the process of bisecting a line segment

When bisecting a line segment \(AB\) using string (similar to compass - and - straightedge construction), the first step is usually to draw an arc centered at one of the endpoints (say \(A\)).

Step2: Analyze each option

• Option A: Setting the string length between point \(A\) and where the arc crosses segment \(AB\) is not a standard step in bisecting the segment.
• Option B: Setting the string length at point \(A\) and at the top of the arc is not relevant to bisecting the line segment \(AB\).
• Option C: Drawing a perpendicular line before having two intersection points (from arcs centered at \(A\) and \(B\)) is premature.
• Option D: In the construction of bisecting a line segment (equivalent to the compass - and - straightedge construction where we first draw an arc centered at \(A\) with a certain radius, then we keep the same radius (string length) and draw an arc centered at \(B\)). The intersection points of these two arcs are used to draw the perpendicular bisector.

Answer:

D. Keep the string length and draw an arc centered at point \(B\) that crosses the other arc in two places.