Point
\[\blue{A}\] is at
\[\blue{(-4, 8)}\] and point
\[\green{B}\] is at
\[\green{(6, 7)}\].
What is the midpoint of line segment
\[\overline{AB}\]?
To find the midpoint of segment $\overline{AB}$, we average the coordinates of points $A$ and $B$. The $x$-coordinate of the midpoint is $\frac{(-4) + (6)}{2} = 1$, and the $y$-coordinate of the midpoint is $\frac{(8) + (7)}{2} = 7.5$. Therefore, the midpoint is $\boxed{(1,7.5)}$.
To find the midpoint of a line segment, we can use the midpoint formula. The midpoint formula states that for two points \(\blue{A} = (\blue{x_1}, \blue{y_1})\) and \(\green{B} = (\green{x_2}, \green{y_2})\), the midpoint \(\red{M}\) can be found using the following formula:
\[
\red{M} = \left(\frac{{\blue{x_1} + \green{x_2}}}{2}, \frac{{\blue{y_1} + \green{y_2}}}{2}\right)
\]
Given that \(\blue{A} = (-4, 8)\) and \(\green{B} = (6, 7)\), we can plug these values into the formula to find the midpoint \(\red{M}\):
\[
\red{M} = \left(\frac{{-4 + 6}}{2}, \frac{{8 + 7}}{2}\right)
\]
The midpoint of a line segment is the point that divides the segment into two equal parts. To find the midpoint of line segment AB, we need to find the average of the x-coordinates and the average of the y-coordinates of points A and B.
To find the x-coordinate of the midpoint, we add the x-coordinates of A and B and divide the sum by 2. In this case, the x-coordinate of A is -4, and the x-coordinate of B is 6. So, the x-coordinate of the midpoint is:
\[\frac{(-4 + 6)}{2} = \frac{2}{2} = 1\]
To find the y-coordinate of the midpoint, we add the y-coordinates of A and B and divide the sum by 2. In this case, the y-coordinate of A is 8, and the y-coordinate of B is 7. So, the y-coordinate of the midpoint is:
\[\frac{(8 + 7)}{2} = \frac{15}{2} = 7.5\]
Therefore, the midpoint of line segment AB is (1, 7.5).