Answer
See graph. Distance is 10 and midpoint is at (3, 12)
Work Step by Step
First we plot out our two points as shown in red and connect them. Next we need to make this into a triangle so we draw another point using the x of one point and the y of the other (shown in blue) at (6, 8).
To use the pythagorean theorem we need to get the distance between our red points and blue point.
So length of A is 16-8 = 8
and length of B = 6-0 = 6
Now we can calculate $A^2 + B^2 = C^2$
$8^2 + 6^2 = C^2$
$64 + 36 = C^2$
$100 = C^2$
$10 = C$
So now we have our distance.
Next to get the midpoint we use the formula:
$\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}$
Plug in our numbers and we get:
$\frac{0+6}{2}, \frac{8+16}{2}$
$\frac{6}{2}, \frac{24}{2}$
Giving us our midpoint coordinates of (3, 12)
