The midpoint of a line segment is the point exactly halfway between two endpoints. Find it by averaging the $x$-coordinates and the $y$-coordinates separately.
$$M = \left(\frac{x_1 + x_2}{2},\ \frac{y_1 + y_2}{2}\right)$$
Example: Find the midpoint of $A(2, 5)$ and $B(8, 1)$: $$M = \left(\frac{2+8}{2},\ \frac{5+1}{2}\right) = (5, 3)$$
Working backwards: if you are given the midpoint $M$ and one endpoint $A$, find the other endpoint $B$ by rearranging — double the midpoint coordinates and subtract the known endpoint.
Example: $M = (4, 6)$, $A = (1, 2)$, find $B$: $$B = (2 \times 4 - 1,\ 2 \times 6 - 2) = (7, 10)$$
Common error: subtracting rather than adding when finding the midpoint, or forgetting to divide by 2.