Midpoint formula

The midpoint of a line segment is the point exactly halfway between its two endpoints.
You find it by averaging the coordinates: $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$.

Work with each coordinate on its own.
Add the two $x$-values and divide by $2$ to get the midpoint's $x$, then do the same with the two $y$-values.
For $(2, 3)$ and $(8, 7)$, that is $\left(\frac{2 + 8}{2}, \frac{3 + 7}{2}\right) = (5, 5)$.

A common use is finding the center of a circle from the endpoints of a diameter.
Since the center is exactly halfway across, it is the midpoint of the two diameter endpoints.

You can also work backwards.
If you know the midpoint and one endpoint, the other endpoint is the same distance away on the far side, which you can find by solving the midpoint equations.

What is the midpoint of the segment from $(2, 3)$ to $(8, 7)$?
Average the coordinates: $\left(\frac{2 + 8}{2}, \frac{3 + 7}{2}\right)$.
So the midpoint is $(5, 5)$.

A circle's diameter has endpoints $(5, -8)$ and $(4, -26)$. What is the center?
The center is the midpoint of the diameter: $\left(\frac{5 + 4}{2}, \frac{-8 + (-26)}{2}\right)$.
So the center is $\left(\frac{9}{2}, -17\right) = (4.5, -17)$.

The midpoint of a segment is $(6, 4)$, and one endpoint is $(2, 1)$. What is the other endpoint?
For the $x$: $\frac{2 + x}{2} = 6$, so $x = 10$; for the $y$: $\frac{1 + y}{2} = 4$, so $y = 7$.
So the other endpoint is $(10, 7)$.