We will examine the midpoint and the length separately.

Midpoint

To find the midpoint of a segment, we can start by examining the distance between the endpoints in the $x -$ and $y -$ direction separately. As an example, we could use the line segment between the points $A (2, 2)$ and $B (8, 4) .$

We can now find the midpoint of $\overline{A B}$ by identifying the midpoint of the vertical and horizontal segments.

This gives us the coordinates for the midpoint of $\overline{A B} .$ In this case, it is $(5, 3) .$

Length

We will use the same segment as above to demonstrate how to find the length. To find the length of $\overline{A B},$ we again use the distances in the $x -$ and $y -$ directions. They are $6$ and $2$ units, respectively.

The three line segments create a right triangle where $\overline{A B}$ is the hypotenuse. Therefore, we can use the Pythagorean Theorem to find the length. The lengths of the legs are $6$ and $2$ units, as stated earlier, so we can substitute $a = 6$ and $b = 2$ to solve for $c .$

Exercise