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?(1 point)

Answer 1

To solve the problem, let's start by understanding the segments.

1. The original segment \( AB \) has a length of 16 centimeters.
2. This segment is bisected at point \( O \), meaning:
\[
AO = OB = \frac{AB}{2} = \frac{16 \, \text{cm}}{2} = 8 \, \text{cm}
\]

3. Next, we bisect segments \( AO \) and \( BO \).

For segment \( AO \):
- The length of \( AO \) is 8 cm.
- When we bisect \( AO \), we denote the midpoint of \( AO \) as \( M \). Thus:
\[
AM = MO = \frac{AO}{2} = \frac{8 \, \text{cm}}{2} = 4 \, \text{cm}
\]

For segment \( BO \):
- The length of \( BO \) is also 8 cm.
- When we bisect \( BO \), we denote the midpoint of \( BO \) as \( N \). Thus:
\[
BN = NO = \frac{BO}{2} = \frac{8 \, \text{cm}}{2} = 4 \, \text{cm}
\]

Thus, each new segment, \( AM \), \( MO \), \( BN \), and \( NO \) measures 4 centimeters. Therefore, the answer is:

**Each new segment is 4 centimeters long.**