Question

what is the coordinate of the midpoint of \\(\overline{mn}\\)?
write your answer as an integer or a decimal, or mixed number in simplest form.

Explanation:

Step1: Identify coordinates of M and N

From the number line, \( M \) is at \( 8 \) and \( N \) is at \( 10 \).

Step2: Use midpoint formula

The midpoint formula for two points \( x_1 \) and \( x_2 \) is \( \frac{x_1 + x_2}{2} \). Substituting \( x_1 = 8 \) and \( x_2 = 10 \), we get \( \frac{8 + 10}{2} \).

Step3: Calculate the midpoint

First, add \( 8 \) and \( 10 \): \( 8 + 10 = 18 \). Then divide by \( 2 \): \( \frac{18}{2} = 9 \). Wait, no, wait. Wait, \( 8 \) and \( 10 \)? Wait, no, looking back, \( M \) is at \( 8 \), \( N \) is at \( 10 \)? Wait, no, the number line: 4,5,6,7,8 (M),9,10 (N). So M is 8, N is 10. Then midpoint is (8 + 10)/2 = 18/2 = 9? Wait, no, that can't be. Wait, no, maybe I misread. Wait, no, 8 and 10: the midpoint between 8 and 10 is 9? Wait, 8 to 9 is 1, 9 to 10 is 1. Yes, so midpoint is 9. Wait, but let's check again. Wait, maybe I made a mistake. Wait, 8 and 10: average is (8 + 10)/2 = 9. Yes, that's correct.

Wait, no, wait, maybe the points are different? Wait, the number line: M is at 8, N is at 10. So midpoint is (8 + 10)/2 = 9. So the midpoint is 9.

Answer:

9