Question

A 16-centimeter segment, AB¯¯¯¯¯¯¯¯ , is bisected at point O . Then, those segments, AO¯¯¯¯¯¯¯¯ and BO¯¯¯¯¯¯¯¯ , are bisected. How long is each new segment

Answer 1

To solve this problem, we start with the initial segment \( AB \), which is 16 centimeters long. When we bisect this segment at point \( O \), we divide it into two equal segments:

\[
AO = BO = \frac{AB}{2} = \frac{16 \text{ cm}}{2} = 8 \text{ cm}
\]

Next, we bisect both segments \( AO \) and \( BO \) at their midpoints. Let's denote the midpoint of \( AO \) as \( M \) and the midpoint of \( BO \) as \( N \).

Now we calculate the lengths of the new segments \( AM \), \( MO \), \( BN \), and \( NO \):

1. For segment \( AO \):
\[
AM = MO = \frac{AO}{2} = \frac{8 \text{ cm}}{2} = 4 \text{ cm}
\]

2. For segment \( BO \):
\[
BN = NO = \frac{BO}{2} = \frac{8 \text{ cm}}{2} = 4 \text{ cm}
\]

Thus, each of the new segments \( AM \), \( MO \), \( BN \), and \( NO \) is 4 centimeters long.

In summary, each new segment resulting from the bisection of segment \( AO \) and segment \( BO \) is:

\[
\text{Each new segment is } 4 \text{ centimeters long.}
\]