Numerically, the midpoint of a segment can be considered to be the average of its endpoints. This concept helps in remembering a formula for finding the midpoint of a segment given the coordinates of its endpoints. Recall that the average of two numbers is found by dividing their sum by two.

*Theorem 102:* If the coordinates of *A* and *B* are ( *x* _{1}, *y* _{1}) and ( *x* _{2}, *y* _{2}) respectively, then the midpoint, *M*, of *AB* is given by the following formula *(Midpoint Formula).*

**Example 1:** In Figure 1*R* is the midpoint between *Q*(−9, −1) and *T*(−3, 7). Find its coordinates and use the *Distance Formula* to verify that it is in fact the midpoint of *QT* .

Figure 1Finding the coordinates of the midpoint of a line segment.

By the *Midpoint Formula,*

By the *Distance Formula,*

Because *QR* = *TR* and *Q, T,* and *R* are collinear, *R* is the midpoint of *QT*

**Example 2:** If the midpoint of *AB* is (−3, 8) and *A* is (12, −1), find the coordinates of *B.*

Let the coordinates of *B* be ( *x, y*). Then by the *Midpoint Formula*,

Multiply each side of each equation by 2.

Therefore, the coordinates of *B* are (−18, 17).