Answer :
To find the midpoint of a line segment with given endpoints, we use the midpoint formula. The formula for the midpoint [tex]\((x_m, y_m)\)[/tex] of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ \left( x_m, y_m \right) = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Given the endpoints [tex]\((3.2, 2.5)\)[/tex] and [tex]\((1.6, -4.5)\)[/tex]:
1. Calculate the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[ x_m = \frac{x_1 + x_2}{2} = \frac{3.2 + 1.6}{2} = \frac{4.8}{2} = 2.4 \][/tex]
2. Calculate the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[ y_m = \frac{y_1 + y_2}{2} = \frac{2.5 - 4.5}{2} = \frac{-2}{2} = -1 \][/tex]
Therefore, the coordinates of the midpoint are [tex]\((2.4, -1)\)[/tex].
Thus, the correct answer is:
A. [tex]\((2.4, -1)\)[/tex]
[tex]\[ \left( x_m, y_m \right) = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Given the endpoints [tex]\((3.2, 2.5)\)[/tex] and [tex]\((1.6, -4.5)\)[/tex]:
1. Calculate the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[ x_m = \frac{x_1 + x_2}{2} = \frac{3.2 + 1.6}{2} = \frac{4.8}{2} = 2.4 \][/tex]
2. Calculate the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[ y_m = \frac{y_1 + y_2}{2} = \frac{2.5 - 4.5}{2} = \frac{-2}{2} = -1 \][/tex]
Therefore, the coordinates of the midpoint are [tex]\((2.4, -1)\)[/tex].
Thus, the correct answer is:
A. [tex]\((2.4, -1)\)[/tex]
