Point
\[\blue{A}\] is at
\[\blue{(-2, -7)}\] and point
\[\green{B}\] is at
\[\green{(7, 4)}\].
What is the midpoint of line segment
\[\overline{AB}\]?
To find the midpoint of a line segment, we average the $x$-coordinates and the $y$-coordinates of the endpoints. The midpoint of $\overline{AB}$ is therefore $\left(\frac{-2+7}{2}, \frac{-7+4}{2}\right) = \boxed{(2.5, -1.5)}$.
To find the midpoint of a line segment, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint are the averages of the coordinates of the two endpoints.
In this case, the coordinates of point A are (-2, -7) and the coordinates of point B are (7, 4). Using the midpoint formula, we can find the coordinates of the midpoint as follows:
1. Find the average of the x-coordinates:
\[(x_{\text{midpoint}}) = \frac{{x_1 + x_2}}{2}\]
\[(x_{\text{midpoint}}) = \frac{{(-2) + (7)}}{2}\]
\[(x_{\text{midpoint}}) = \frac{{5}}{2}\]
2. Find the average of the y-coordinates:
\[(y_{\text{midpoint}}) = \frac{{y_1 + y_2}}{2}\]
\[(y_{\text{midpoint}}) = \frac{{(-7) + (4)}}{2}\]
\[(y_{\text{midpoint}}) = \frac{{-3}}{2}\]
So, the midpoint of the line segment AB is \(\left(\frac{5}{2}, -\frac{3}{2}\right)\).
To find the midpoint of line segment $\overline{AB}$, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints $\blue{(x_1, y_1)}$ and $\green{(x_2, y_2)}$ are given by:
\[\left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right)\]
Now let's apply the formula to determine the midpoint of line segment $\overline{AB}$:
The coordinates of point $\blue{A}$ are $\blue{(-2, -7)}$, and the coordinates of point $\green{B}$ are $\green{(7, 4)}$.
Using the midpoint formula, we get:
\[x_{\text{mid}} = \frac{{-2 + 7}}{2} = 2.5\]
\[y_{\text{mid}} = \frac{{-7 + 4}}{2} = -1.5\]
Therefore, the midpoint of line segment $\overline{AB}$ is $\left(2.5, -1.5\right)$.