To find the midpoint of a line segment with given endpoints, we use the midpoint formula. If the endpoints are [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex], the coordinates of the midpoint [tex]\((M)\)[/tex] can be calculated as follows:
[tex]\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Given the endpoints [tex]\((-1, 7)\)[/tex] and [tex]\((3, -3)\)[/tex], let's identify [tex]\(x_1\)[/tex], [tex]\(y_1\)[/tex], [tex]\(x_2\)[/tex], and [tex]\(y_2\)[/tex]:
- [tex]\( x_1 = -1 \)[/tex]
- [tex]\( y_1 = 7 \)[/tex]
- [tex]\( x_2 = 3 \)[/tex]
- [tex]\( y_2 = -3 \)[/tex]
Now we apply the midpoint formula step-by-step:
1. Calculate the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[
\frac{x_1 + x_2}{2} = \frac{-1 + 3}{2} = \frac{2}{2} = 1
\][/tex]
2. Calculate the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[
\frac{y_1 + y_2}{2} = \frac{7 + (-3)}{2} = \frac{4}{2} = 2
\][/tex]
Therefore, the coordinates of the midpoint are [tex]\((1, 2)\)[/tex].
The correct answer is:
A. [tex]\((1, 2)\)[/tex]
