Question

find the location of b, the midpoint of \\( \overline { a c } \\).

Explanation:

Step1: Recall the mid - point formula

The mid - point formula for two points \(x_1\) and \(x_2\) on a number line is \(B=\frac{x_1 + x_2}{2}\). Here, if \(A=-7\) (since \(A\) is at \(-7\) on the number line) and \(C = 1\) (since \(C\) is at \(1\) on the number line).

Step2: Substitute the values into the formula

Substitute \(x_1=-7\) and \(x_2 = 1\) into the formula \(B=\frac{x_1+x_2}{2}\). So, \(B=\frac{-7 + 1}{2}\).
First, calculate the numerator: \(-7+1=-6\). Then, divide by \(2\): \(\frac{-6}{2}=-3\).

Answer:

\(-3\)