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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)

1 answer

To solve the problem, we start with the original segment \( AB \), which has a length of 16 centimeters.

  1. Bisecting Segment AB:

    • When \( AB \) is bisected at point \( O \), we divide the segment into two equal parts, \( AO \) and \( BO \).
    • The length of each segment \( AO \) and \( BO \) is: \[ AO = BO = \frac{16 \text{ cm}}{2} = 8 \text{ cm} \]

  2. Bisecting Segments AO and BO:

    • Next, we bisect each of the segments \( AO \) and \( BO \).
    • For segment \( AO \), bisecting it at point \( M \) (the midpoint of \( AO \)), each new segment \( AM \) and \( MO \) will have a length of: \[ AM = MO = \frac{8 \text{ cm}}{2} = 4 \text{ cm} \]
    • For segment \( BO \), bisecting it at point \( N \) (the midpoint of \( BO \)), each new segment \( BN \) and \( NO \) will also have a length of: \[ BN = NO = \frac{8 \text{ cm}}{2} = 4 \text{ cm} \]

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

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