$¯ ¯¯¯¯¯¯¯¯¯ ¯ M N$ is the perpendicular bisector of the line segment $¯ ¯¯¯¯¯¯ ¯ A B$ . If $¯ ¯¯¯¯¯¯ ¯ A B$ measures 6 cm, what is the length of $¯ ¯¯¯¯¯¯¯ ¯ A N$ and $¯ ¯¯¯¯¯¯¯ ¯ N B$ ?

¯ ¯¯¯¯¯¯¯ ¯ A N = ¯ ¯¯¯¯¯¯¯ ¯ N B = 6 c m

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¯ ¯¯¯¯¯¯¯ ¯ A N = 3 c m

and

¯ ¯¯¯¯¯¯¯ ¯ N B = 4 c m

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¯ ¯¯¯¯¯¯¯ ¯ A N = ¯ ¯¯¯¯¯¯¯ ¯ N B = 3 c m

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¯ ¯¯¯¯¯¯¯ ¯ A N = 6 c m

and

¯ ¯¯¯¯¯¯¯ ¯ N B = 3 c m

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Solution

The correct option is C $¯ ¯¯¯¯¯¯¯ ¯ A N = ¯ ¯¯¯¯¯¯¯ ¯ N B = 3 c m$
In the given figure, $¯ ¯¯¯¯¯¯ ¯ A B = 6 c m$ .

Since, $¯ ¯¯¯¯¯¯¯¯¯ ¯ M N$ is the perpendicular bisector of $¯ ¯¯¯¯¯¯ ¯ A B$ , $¯ ¯¯¯¯¯¯¯¯¯ ¯ M N$ bisects the line $¯ ¯¯¯¯¯¯ ¯ A B$ .
$\Rightarrow ¯ ¯¯¯¯¯¯¯ ¯ A N = ¯ ¯¯¯¯¯¯¯ ¯ N B$

$¯ ¯¯¯¯¯¯¯ ¯ A N = \frac{¯ ¯¯¯¯¯ ¯ A B}{2} = \frac{6 c m}{2} = 3 c m$

So, $¯ ¯¯¯¯¯¯¯ ¯ A N = ¯ ¯¯¯¯¯¯¯ ¯ N B = 3 c m$ .

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