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 at point a and at the top of the arc.
b. set the string length between point a and where the arc crosses segment ab.
c. keep the string length and draw an arc centered at point b that crosses the other arc in two places.
d. using a straightedge, draw a line perpendicular to segment ab so it crosses the arc in two places.

Explanation:

Step1: Recall the steps of bisecting a line segment

When bisecting a line segment \(AB\) using string (similar to using a compass - string acts like the radius of a compass), first, we fix one end of the string at \(A\) and draw an arc.

Step2: Analyze each option

• Option A: Setting the string length at \(A\) and at the top of the arc is not a standard step in bisecting a line segment.
• Option B: Setting the string length between \(A\) and where the arc crosses \(AB\) is not relevant to the bisecting process.
• Option C: After drawing an arc centered at \(A\), the next step is to keep the same string length (radius) and draw an arc centered at \(B\). The intersection points of these two arcs will help us construct the perpendicular bisector.
• Option D: Drawing a perpendicular line using a straightedge before getting the second arc is premature. We need two arcs (one from \(A\) and one from \(B\)) to accurately find the points for the perpendicular bisector.

Answer:

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