Answer :
To determine the midpoint of a line segment whose endpoints are [tex]\((3.5, 2.2)\)[/tex] and [tex]\((1.5, -4.8)\)[/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]
Given the endpoints [tex]\((3.5, 2.2)\)[/tex] and [tex]\((1.5, -4.8)\)[/tex]:
1. Calculate the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[ \frac{3.5 + 1.5}{2} = \frac{5}{2} = 2.5 \][/tex]
2. Calculate the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[ \frac{2.2 + (-4.8)}{2} = \frac{2.2 - 4.8}{2} = \frac{-2.6}{2} = -1.3 \][/tex]
Therefore, the coordinates of the midpoint are:
[tex]\[ (2.5, -1.3) \][/tex]
Thus, the correct answer is [tex]\(\boxed{(2.5, -1.3)}\)[/tex]. This matches option B.
[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Given the endpoints [tex]\((3.5, 2.2)\)[/tex] and [tex]\((1.5, -4.8)\)[/tex]:
1. Calculate the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[ \frac{3.5 + 1.5}{2} = \frac{5}{2} = 2.5 \][/tex]
2. Calculate the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[ \frac{2.2 + (-4.8)}{2} = \frac{2.2 - 4.8}{2} = \frac{-2.6}{2} = -1.3 \][/tex]
Therefore, the coordinates of the midpoint are:
[tex]\[ (2.5, -1.3) \][/tex]
Thus, the correct answer is [tex]\(\boxed{(2.5, -1.3)}\)[/tex]. This matches option B.
