Answer :
To find the midpoint of the line segment with endpoints [tex]\((3.2, 2.5)\)[/tex] and [tex]\((1.6, -4.5)\)[/tex], we use the midpoint formula. The midpoint formula for two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Let's apply this formula step by step:
1. Identify the coordinates of the endpoints:
[tex]\[ (x_1, y_1) = (3.2, 2.5) \][/tex]
[tex]\[ (x_2, y_2) = (1.6, -4.5) \][/tex]
2. Calculate the x-coordinate of the midpoint:
[tex]\[ \frac{x_1 + x_2}{2} = \frac{3.2 + 1.6}{2} = \frac{4.8}{2} = 2.4 \][/tex]
3. Calculate the y-coordinate of the midpoint:
[tex]\[ \frac{y_1 + y_2}{2} = \frac{2.5 + (-4.5)}{2} = \frac{2.5 - 4.5}{2} = \frac{-2}{2} = -1 \][/tex]
Therefore, the coordinates of the midpoint are:
[tex]\[ (2.4, -1) \][/tex]
From the given options, the correct answer is:
C. [tex]\((2.4, -1)\)[/tex]
[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Let's apply this formula step by step:
1. Identify the coordinates of the endpoints:
[tex]\[ (x_1, y_1) = (3.2, 2.5) \][/tex]
[tex]\[ (x_2, y_2) = (1.6, -4.5) \][/tex]
2. Calculate the x-coordinate of the midpoint:
[tex]\[ \frac{x_1 + x_2}{2} = \frac{3.2 + 1.6}{2} = \frac{4.8}{2} = 2.4 \][/tex]
3. Calculate the y-coordinate of the midpoint:
[tex]\[ \frac{y_1 + y_2}{2} = \frac{2.5 + (-4.5)}{2} = \frac{2.5 - 4.5}{2} = \frac{-2}{2} = -1 \][/tex]
Therefore, the coordinates of the midpoint are:
[tex]\[ (2.4, -1) \][/tex]
From the given options, the correct answer is:
C. [tex]\((2.4, -1)\)[/tex]
