To find the midpoint of a line segment with given endpoints, we use the midpoint formula. The midpoint formula states that the coordinates of the midpoint [tex]\((M_x, M_y)\)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] can be calculated as follows:
[tex]\[ M_x = \frac{x_1 + x_2}{2} \][/tex]
[tex]\[ M_y = \frac{y_1 + y_2}{2} \][/tex]
Given the endpoints of the line segment are [tex]\((3.2, 2.5)\)[/tex] and [tex]\((1.6, -4.5)\)[/tex]:
First, we calculate the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[ M_x = \frac{3.2 + 1.6}{2} \][/tex]
Next, we calculate the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[ M_y = \frac{2.5 + (-4.5)}{2} \][/tex]
Summing the [tex]\(x\)[/tex]-coordinates:
[tex]\[ 3.2 + 1.6 = 4.8 \][/tex]
Now, finding the average for [tex]\(M_x\)[/tex]:
[tex]\[ M_x = \frac{4.8}{2} = 2.4 \][/tex]
Summing the [tex]\(y\)[/tex]-coordinates:
[tex]\[ 2.5 + (-4.5) = 2.5 - 4.5 = -2.0 \][/tex]
Now, finding the average for [tex]\(M_y\)[/tex]:
[tex]\[ M_y = \frac{-2.0}{2} = -1.0 \][/tex]
Therefore, the coordinates of the midpoint are:
[tex]\[ (2.4, -1.0) \][/tex]
So, the answer is:
C. [tex]\((2.4, -1)\)[/tex]
