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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 find the lengths of each new segment after bisecting the original 16-centimeter segment \( AB \), we can follow these steps:

  1. Bisect the original segment \( AB \) at point \( O \): The segment \( AB \) is 16 cm long. When it is bisected at \( O \), each segment \( AO \) and \( OB \) will be half of 16 cm: \[ AO = OB = \frac{16 \text{ cm}}{2} = 8 \text{ cm} \]

  2. Bisect the segments \( AO \) and \( OB \): Next, we bisect the segments \( AO \) and \( OB \) at points let's call \( C \) and \( D \) respectively.

    • The segment \( AO \) (which is 8 cm) is bisected: \[ AC = OC = \frac{8 \text{ cm}}{2} = 4 \text{ cm} \]
    • The segment \( OB \) (also 8 cm) is bisected: \[ OD = OB = \frac{8 \text{ cm}}{2} = 4 \text{ cm} \]

So, after bisecting the segments \( AO \) and \( OB \), each new segment \( AC \), \( OC \), \( OD \), and \( DB \) is 4 cm long.

Final Answer: Each new segment is 4 centimeters long.