To find the midpoint of a line segment with given endpoints [tex]\((-1,7)\)[/tex] and [tex]\( (3,-3) \)[/tex], we use the midpoint formula. The midpoint [tex]\(M\)[/tex] of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Let's apply the formula step by step:
1. Identify the coordinates of the endpoints:
- [tex]\((x_1, y_1) = (-1, 7)\)[/tex]
- [tex]\((x_2, y_2) = (3, -3)\)[/tex]
2. Substitute the coordinates into the midpoint formula:
[tex]\[ M_x = \frac{-1 + 3}{2} \][/tex]
[tex]\[ M_y = \frac{7 + (-3)}{2} \][/tex]
3. Calculate each part separately:
[tex]\[ M_x = \frac{-1 + 3}{2} = \frac{2}{2} = 1 \][/tex]
[tex]\[ M_y = \frac{7 + (-3)}{2} = \frac{4}{2} = 2 \][/tex]
4. Combine the results to get the coordinates of the midpoint:
[tex]\[ M = (1, 2) \][/tex]
Therefore, the midpoint of the line segment with endpoints [tex]\((-1, 7)\)[/tex] and [tex]\( (3, -3)\)[/tex] is [tex]\(\boxed{(1, 2)}\)[/tex]. Thus, the correct answer is:
[tex]\[ B.\ (1,2) \][/tex]
