To find the coordinates of the midpoint of the line segment joining the points [tex]\((2,4)\)[/tex] and [tex]\((-2,-1)\)[/tex], we use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint, [tex]\(M(x_m, y_m)\)[/tex], between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ M(x_m, y_m) = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Given the points:
[tex]\[
(x_1, y_1) = (2, 4) \quad \text{and} \quad (x_2, y_2) = (-2, -1)
\][/tex]
We can substitute these values into the midpoint formula:
1. Calculate the x-coordinate of the midpoint:
[tex]\[
x_m = \frac{x_1 + x_2}{2} = \frac{2 + (-2)}{2} = \frac{2 - 2}{2} = \frac{0}{2} = 0.0
\][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[
y_m = \frac{y_1 + y_2}{2} = \frac{4 + (-1)}{2} = \frac{4 - 1}{2} = \frac{3}{2} = 1.5
\][/tex]
So, the coordinates of the midpoint are:
[tex]\[
(0.0, 1.5)
\][/tex]
Thus, the midpoint of the line segment joining the points [tex]\((2, 4)\)[/tex] and [tex]\((-2, -1)\)[/tex] is [tex]\((0.0, 1.5)\)[/tex].
