Question

A 16-centimeter segment, AB¯¯¯¯¯¯¯¯
𝐴
𝐵
¯
, is bisected at point O
𝑂
. Then, those segments, AO¯¯¯¯¯¯¯¯
𝐴
𝑂
¯
and BO¯¯¯¯¯¯¯¯
𝐵
𝑂
¯
, are bisected. How long is each new segment?(1 point

Answer 1

To find the lengths of the segments after consecutive bisections, we start with the original segment \( AB \) which is 16 centimeters long.

1. **First bisection at point O:**
\[
AO = \frac{AB}{2} = \frac{16 \text{ cm}}{2} = 8 \text{ cm}
\]
\[
BO = \frac{AB}{2} = 8 \text{ cm}
\]

2. **Second bisection of segment \( AO \) at point M:**
\[
AM = \frac{AO}{2} = \frac{8 \text{ cm}}{2} = 4 \text{ cm}
\]
\[
OM = \frac{AO}{2} = 4 \text{ cm}
\]

3. **Second bisection of segment \( BO \) at point N:**
\[
BN = \frac{BO}{2} = \frac{8 \text{ cm}}{2} = 4 \text{ cm}
\]
\[
ON = \frac{BO}{2} = 4 \text{ cm}
\]

Thus, after the first bisection \( AO \) and \( BO \) are each 8 cm, and after the second bisections \( AM \) and \( OM \) are each 4 cm, as are \( BN \) and \( ON \).

Overall, each new segment \( AM, OM, BN, \) and \( ON \) are 4 cm long.