To find the midpoint of two points [tex]\(A\)[/tex] and [tex]\(B\)[/tex], we use the midpoint formula. The midpoint [tex]\(M\)[/tex] of two points [tex]\(A(x_1, y_1)\)[/tex] and [tex]\(B(x_2, y_2)\)[/tex] is given by:
[tex]\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Given the coordinates of point [tex]\(A\)[/tex] as [tex]\((-7, 1)\)[/tex] and point [tex]\(B\)[/tex] as [tex]\((3, -5)\)[/tex], we will substitute these values into the formula.
1. For the [tex]\(x\)[/tex]-coordinates:
[tex]\[
x_{\text{mid}} = \frac{-7 + 3}{2}
\][/tex]
Calculate the sum inside the numerator:
[tex]\[
-7 + 3 = -4
\][/tex]
Next, divide by 2:
[tex]\[
x_{\text{mid}} = \frac{-4}{2} = -2
\][/tex]
2. For the [tex]\(y\)[/tex]-coordinates:
[tex]\[
y_{\text{mid}} = \frac{1 + (-5)}{2}
\][/tex]
Calculate the sum inside the numerator:
[tex]\[
1 + (-5) = 1 - 5 = -4
\][/tex]
Next, divide by 2:
[tex]\[
y_{\text{mid}} = \frac{-4}{2} = -2
\][/tex]
Thus, the coordinates of the midpoint [tex]\(M\)[/tex] are:
[tex]\[
M = (-2, -2)
\][/tex]
