Question

use the figure to the right to find the length of \\( \overline{mb} \\).

the length of \\( \overline{mb} \\) is \\( \square \\) units. (type an integer or a decimal.)

Explanation:

Step1: Analyze the figure

Since \( AM = MB \) (the line \( NM \) is the perpendicular bisector of \( AB \)), we can directly use the property of perpendicular bisector.

Step2: Determine the length

From the figure, we can see that \( AM = 3 \) (given in the figure). But wait, no! Wait, looking at the right - triangle \( PMB \), using the Pythagorean theorem \( PM^{2}+MB^{2}=PB^{2}\). But wait, no, wait the figure shows that \( AM = MB \) (because of the congruent segments marked on \( AB \) with respect to the perpendicular bisector \( NM \)). So \( MB=3 \) units.

Answer:

\( 3 \)